Precalculus: Mathematics for Calculus (Standalone Book)
7th Edition
ISBN: 9781305071759
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Brooks Cole
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Textbook Question
Chapter 4.6, Problem 5E
Population Growth These exercises use the population growth model.
5. Fox Population The fox population in a certain region has a relative growth rate of 8% per year. It is estimated that the population in 2013 was 18,000.
- (a) Find a function n(t) = n0ert that models the population t years after 2013.
- (b) Use the function from part (a) to estimate the fox population in the year 2021.
- (c) After how many years will the fox population reach 25,000?
- (d) Sketch a graph of the fox population function for the years 2013–2021.
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Precalculus: Mathematics for Calculus (Standalone Book)
Ch. 4.1 - The function f(x) = 5x is an exponential function...Ch. 4.1 - Match the exponential function with one of the...Ch. 4.1 - (a) To obtain the graph of g(x) = 2x 1, we start...Ch. 4.1 - In the formula A(t)=P(1+rn)nt for compound...Ch. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Evaluating Exponential Functions Use a calculator...Ch. 4.1 - Evaluating Exponential Functions Use a calculator...Ch. 4.1 - Prob. 9ECh. 4.1 - Evaluating Exponential Functions Use a calculator...
Ch. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Prob. 12ECh. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Prob. 14ECh. 4.1 - Graphing Exponential Functions Sketch the graph of...Ch. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Prob. 22ECh. 4.1 - Exponential Functions from a Graph Find the...Ch. 4.1 - Prob. 24ECh. 4.1 - Exponential Functions from a Graph Match the...Ch. 4.1 - Exponential Functions from a Graph Match the...Ch. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 28ECh. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 30ECh. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 32ECh. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 34ECh. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 36ECh. 4.1 - Graphing Exponential Functions Graph the function,...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Comparing Exponential Functions In these exercises...Ch. 4.1 - Comparing Exponential and Power Functions Compare...Ch. 4.1 - Comparing Exponential and Power Functions Compare...Ch. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Families of Functions Draw graphs of the given...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Difference Quotients These exercises involve a...Ch. 4.1 - Prob. 52ECh. 4.1 - Bacteria Growth A bacteria culture contains 1500...Ch. 4.1 - Mouse Population A certain breed of mouse was...Ch. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Compound Interest If 10,000 is invested at an...Ch. 4.1 - Compound Interest If 2500 is invested at an...Ch. 4.1 - Compound Interest If 500 is invested at an...Ch. 4.1 - Compound Interest If 4000 is borrowed at a rate of...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.2 - The function f(x) = ex is called the __________...Ch. 4.2 - In the formula A(t) = Pert for continuously...Ch. 4.2 - Evaluating Exponential Functions Use a calculator...Ch. 4.2 - Evaluating Exponential Functions Use a calculator...Ch. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Prob. 8ECh. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Prob. 10ECh. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Prob. 12ECh. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Prob. 14ECh. 4.2 - Graphing Exponential Functions Graph the function,...Ch. 4.2 - Prob. 16ECh. 4.2 - Hyperbolic Cosine Function The hyperbolic cosine...Ch. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Medical Drugs When a certain medical drug is...Ch. 4.2 - Radioactive Decay A radioactive substance decays...Ch. 4.2 - Sky Diving A sky diver jumps from a reasonable...Ch. 4.2 - Mixtures and Concentrations A 50-gal barrel is...Ch. 4.2 - Logistic Growth Animal populations are not capable...Ch. 4.2 - Bird Population The population of a certain...Ch. 4.2 - World Population The relative growth rate of world...Ch. 4.2 - Tree Diameter For a certain type of tree the...Ch. 4.2 - Prob. 31ECh. 4.2 - Compound Interest An investment of 7000 is...Ch. 4.2 - Compound Interest If 2000 is invested at an...Ch. 4.2 - Compound Interest If 3500 is invested at an...Ch. 4.2 - Compound Interest If 600 is invested at an...Ch. 4.2 - Prob. 36ECh. 4.2 - Compound Interest Which of the given interest...Ch. 4.2 - Prob. 38ECh. 4.2 - Investment A sum of 5000 is invested at an...Ch. 4.3 - log x is the exponent to which the base 10 must be...Ch. 4.3 - The function f(x) = log9 x is the logarithm...Ch. 4.3 - Prob. 3ECh. 4.3 - Match the logarithmic function with its graph. (a)...Ch. 4.3 - The natural logarithmic function f(x) = ln x has...Ch. 4.3 - The logarithmic function f(x) = ln(x 1) has the...Ch. 4.3 - Logarithmic and Exponential Forms Complete the...Ch. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Exponential Form Express the equation in...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Evaluating Logarithms Evaluate the expression. 28....Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Finding Logarithmic Functions Find the function of...Ch. 4.3 - Prob. 57ECh. 4.3 - Graphing Logarithmic Functions Match the...Ch. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Graphing Logarithmic Functions Graph the function,...Ch. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Domain of a Composition Find the functions f g...Ch. 4.3 - Prob. 88ECh. 4.3 - Prob. 89ECh. 4.3 - Prob. 90ECh. 4.3 - Prob. 91ECh. 4.3 - Prob. 92ECh. 4.3 - Prob. 93ECh. 4.3 - Prob. 94ECh. 4.3 - Prob. 95ECh. 4.3 - Absorption of Light A spectrophotometer measures...Ch. 4.3 - Carbon Dating The age of an ancient artifact can...Ch. 4.3 - Bacteria Colony A certain strain of bacteria...Ch. 4.3 - Prob. 99ECh. 4.3 - Charging a Battery The rate at which a battery...Ch. 4.3 - Difficulty of a Task The difficulty in acquiring a...Ch. 4.3 - Prob. 102ECh. 4.3 - Prob. 103ECh. 4.3 - Prob. 104ECh. 4.3 - DISCUSS DISCOVER: The Number of Digits in an...Ch. 4.4 - The logarithm of a product of two numbers is the...Ch. 4.4 - The logarithm of a quotient of two numbers is the...Ch. 4.4 - The logarithm of a number raised to a power is the...Ch. 4.4 - Prob. 4ECh. 4.4 - We can combine 2 log x + log y log z to get...Ch. 4.4 - Prob. 6ECh. 4.4 - True or False? 7. (a) log(A + B) is the same as...Ch. 4.4 - (a) logAB is the same as log A log B. (b) logAB...Ch. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Prob. 10ECh. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Prob. 12ECh. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Evaluating Logarithms Use the Laws of Logarithms...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 30ECh. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Expanding Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 54ECh. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Combining Logarithmic Expressions Use the Laws of...Ch. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Change of Base Formula Use the Change of Base...Ch. 4.4 - Change of Base Formula Simplify: (log2 5)(log5 7)Ch. 4.4 - Prob. 71ECh. 4.4 - Forgetting Use the Law of Forgetting (Example 4)...Ch. 4.4 - Wealth Distribution Vilfredo Pareto (18481923)...Ch. 4.4 - Biodiversity Some biologists model the number of...Ch. 4.4 - Magnitude of Stars The magnitude M of a star is a...Ch. 4.4 - DISCUSS: True or False? Discuss each equation, and...Ch. 4.4 - Prob. 77ECh. 4.4 - PROVE: Shifting, Shrinking, and Stretching Graphs...Ch. 4.5 - Lets solve the exponential equation 2ex = 50. (a)...Ch. 4.5 - Lets solve the logarithmic equation...Ch. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Prob. 4ECh. 4.5 - Exponential Equations Find the solution of the...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 36ECh. 4.5 - Exponential Equations (a) Find the exact solution...Ch. 4.5 - Prob. 38ECh. 4.5 - Exponential Equations of Quadratic Type Solve the...Ch. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Equations Involving Exponential Functions Solve...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 50ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 52ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 54ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 56ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Logarithmic Equations Solve the logarithmic...Ch. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Prob. 84ECh. 4.5 - Inverse Functions Find the inverse function of f....Ch. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.5 - Compound interest A man invests 5000 in an account...Ch. 4.5 - Compound Interest A woman invests 6500 in an...Ch. 4.5 - Prob. 91ECh. 4.5 - Compound Interest Nancy wants to invest 4000 in...Ch. 4.5 - Doubling an Investment How long will it take for...Ch. 4.5 - Interest Rate A sum of 1000 was invested for 4...Ch. 4.5 - Radioactive Decay A 15-g sample of radioactive...Ch. 4.5 - Sky Diving The velocity of a sky diver t seconds...Ch. 4.5 - Fish Population A small lake is stocked with a...Ch. 4.5 - Transparency of a Lake Environmental scientists...Ch. 4.5 - Atmospheric Pressure Atmospheric pressure P (in...Ch. 4.5 - Cooling an Engine Suppose youre driving your car...Ch. 4.5 - Electric Circuits An electric circuit contains a...Ch. 4.5 - Learning Curve A learning curve is a graph of a...Ch. 4.5 - DISCUSS: Estimating a Solution Without actually...Ch. 4.5 - DISCUSS DISCOVER: A Surprising Equation Take...Ch. 4.5 - DISCUSS: Disguised Equations Each of these...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Prob. 4ECh. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Prob. 8ECh. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Prob. 16ECh. 4.6 - Radioactive Radium The half-life of radium-226 is...Ch. 4.6 - Radioactive Cesium The half-life of cesium-137 is...Ch. 4.6 - Radioactive Strontium The half-life of...Ch. 4.6 - Radioactive Radium Radium-221 has a half-life of...Ch. 4.6 - Finding Half-Life If 250 mg of a radioactive...Ch. 4.6 - Radioactive Radon After 3 days a sample of...Ch. 4.6 - Carbon-14 Dating A wooden artifact from an ancient...Ch. 4.6 - Carbon-14 Dating The burial cloth of an Egyptian...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.7 - Finding pH The hydrogen ion concentration of a...Ch. 4.7 - Prob. 2ECh. 4.7 - Ion Concentration The pH reading of a sample of...Ch. 4.7 - Ion Concentration The pH reading of a glass of...Ch. 4.7 - Finding pH The hydrogen ion concentrations in...Ch. 4.7 - Prob. 6ECh. 4.7 - pH of Wine If the pH of a wine is too high, say,...Ch. 4.7 - pH of Saliva The pH of saliva is normally in the...Ch. 4.7 - Earthquake Magnitude and Intensity (a) Find the...Ch. 4.7 - Earthquake Magnitude and Intensity (a) Find the...Ch. 4.7 - Earthquake Magnitudes If one earthquake is 20...Ch. 4.7 - Earthquake Magnitudes The 1906 earthquake in San...Ch. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Traffic Noise The intensity of the sound of...Ch. 4.7 - Leaf Blower The intensity of the sound from a...Ch. 4.7 - Hair Dryer The decibel level of the sound from a...Ch. 4.7 - Subway Noise The decibel level of the sound of a...Ch. 4.7 - Hearing Loss from MP3 Players Recent research has...Ch. 4.7 - Comparing Decibel Levels The noise from a power...Ch. 4.7 - PROVE: Inverse Square Law for Sound A law of...Ch. 4 - Let f be the exponential function with base a. (a)...Ch. 4 - Prob. 2RCCCh. 4 - Prob. 3RCCCh. 4 - Prob. 4RCCCh. 4 - (a) How is loga x defined? (b) Find log3 9. (c)...Ch. 4 - Prob. 6RCCCh. 4 - Prob. 7RCCCh. 4 - Prob. 8RCCCh. 4 - (a) What is an exponential equation? (b) How do...Ch. 4 - Prob. 10RCCCh. 4 - Prob. 11RCCCh. 4 - Suppose that the initial size of a population is...Ch. 4 - Prob. 13RCCCh. 4 - Prob. 14RCCCh. 4 - Prob. 15RCCCh. 4 - Prob. 16RCCCh. 4 - Prob. 17RCCCh. 4 - Prob. 18RCCCh. 4 - Prob. 1RECh. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Prob. 14RECh. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Exponential Form Write the equation in exponential...Ch. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 33RECh. 4 - Evaluating Logarithmic Expressions Evaluate the...Ch. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 43RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 59RECh. 4 - Prob. 60RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 63RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Prob. 71RECh. 4 - Prob. 72RECh. 4 - Prob. 73RECh. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 77RECh. 4 - Prob. 78RECh. 4 - Prob. 79RECh. 4 - Prob. 80RECh. 4 - Prob. 81RECh. 4 - Prob. 82RECh. 4 - Prob. 83RECh. 4 - Prob. 84RECh. 4 - Prob. 85RECh. 4 - Prob. 86RECh. 4 - Prob. 87RECh. 4 - Prob. 88RECh. 4 - Prob. 89RECh. 4 - Prob. 90RECh. 4 - Prob. 91RECh. 4 - Compound Interest A sum of 5000 is invested at an...Ch. 4 - Compound Interest A money market account pays 5.2%...Ch. 4 - Compound Interest A retirement savings plan pays...Ch. 4 - Prob. 95RECh. 4 - Prob. 96RECh. 4 - Cat Population The stray-cat population in a small...Ch. 4 - Bacterial Growth A culture contains 10,000...Ch. 4 - Radioactive Decay Uranium-234 has a half-life of...Ch. 4 - Prob. 100RECh. 4 - Radioactive Decay The half-life of radium-226 is...Ch. 4 - Radioactive Decay The half-life of palladium-100...Ch. 4 - Bird Population The graph shows the population of...Ch. 4 - Prob. 104RECh. 4 - pH The hydrogen ion concentration of fresh egg...Ch. 4 - pH The pH of lime juice is 1.9. Find the hydrogen...Ch. 4 - Prob. 107RECh. 4 - Prob. 108RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - (a) Write the equation 62x = 25 in logarithmic...Ch. 4 - Find the exact value of the expression. (a) 10log...Ch. 4 - Use the Laws of Logarithms to expand the...Ch. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - The initial size of a culture of bacteria is 1000....Ch. 4 - Suppose that 12,000 is invested in a savings...Ch. 4 - The half-life of krypton-91 (91Kr) is 10 s. At...Ch. 4 - An earthquake measuring 6.4 on the Richter scale...Ch. 4 - U.S. Population The U.S. Constitution requires a...Ch. 4 - A Falling Ball In a physics experiment a lead ball...Ch. 4 - Half-Life of Radioactive Iodine A student is...Ch. 4 - The Beer-Lambert Law As sunlight passes through...Ch. 4 - Prob. 5PCh. 4 - Modeling the Species-Area Relation The table gives...Ch. 4 - Auto Exhaust Emissions A study by the U.S. Office...Ch. 4 - Prob. 8PCh. 4 - Prob. 9PCh. 4 - Logistic Population Growth The table and scatter...
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- Population Growth These exercises use the population growth model. 8. Bacteria Culture It is observed that a certain bacteria culturehas a relative growth rate or 12% hour. but in the presence of an antibiotic the relative growth rate is reduced to 5% per Hour.initialnumber of bacteria in the culture is 22. Population,n after 24 hours for following conditions. (a) No antibiotic is present, so the relative rate is 12%. (b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.arrow_forwardPopulation Growth These exercises use the population growth model. 4. Bird Population A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 13,000. (a) What was initial size Of the bird population? (b) Estimate the bird 5 years from now. (c) Sketch a graph Of the birdarrow_forwardSales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?arrow_forward
- Population Growth These exercises use the population growth model. Frog Population Some bullfrogs were into a small pond. TIE graph bullfrog.population for the next few years. Assume that the population grows (a) What was the initial bullfrog population? (b) Find a function that models the bullfrog Bypopulation t yeas since the bullfrogs were put into pond. (c) What is the projected bullfrogpopulation after 15 years? (d) Estimate how long it takes the population to reach 75,000.arrow_forwardradioactive Decay These exercises use the population radioactive Decay. Radioactive Cesium The half-life of cesium- 37 is 30 years. Suppose we have a sample. (a) Find a function m(t)=m0et/k that mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample Will remain after 80 years? (d) After how many years will only 2 g of the sample remain?arrow_forwardPopulation Growth These exercises use the population growth model. Bacteria Culture A culture starts with 8600 bacteria. After 1 hour the count is 10,000. (a) Find a function that models thenumber Ofbacteria nbacteria n(t) after t hours. (b) Find the number of bacteria after 2 hours. (c) After how many Will Of bacteria double ?arrow_forward
- radioactive Decay These exercises use the population radioactive Decay. Radioactive Radium The half life of radium 226 is 1600 years. Suppose we have a 22-mg sample. (a) Find a function m(t)=m02r/k that models mass remaining after t years. (b) Find a function m(t)=m0ert that models the remaining after t years. (c) How much of sample will remain after 4000 years? (d) After how many years Will only 18 mg Of sample remain?arrow_forwardLogistic Growth Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model: p(t)=d1+kea Where c, d, and k are positive constants. For a certain fish population in a small pond d=1200, k=11, c=0.2, and t is measured in years. The fish were introduced into the pond at time t=0 . How many fish were originally put in the pond? Find the population after 10, 20, and 30 years. Evaluate p(t) for large values of t. What value does the population approach as t? Does the graph shown confirm your calculations?arrow_forward
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