Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Question
Chapter 4.4, Problem 63E
To determine
(a)
To find:
The growth function
To determine
(b)
To find:
The proportion of manuscripts and their rate of growth after the 1 century.
To determine
(c)
To find:
The proportion of manuscripts and their rate of growth after the 2 century.
To determine
(d)
To find:
The proportion of manuscripts and their rate of growth after the 3 century.
To determine
(e)
To explain:
What will happen to the growth rate over a time.
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Calculus For The Life Sciences
Ch. 4.1 - YOUR TURN If ft=1t, find f't.Ch. 4.1 - Prob. 2YTCh. 4.1 - YOUR TURN If ht=-3t2+2t+5t4-7, find h't.Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...
Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Find the derivative of each function defined as...Ch. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Which of the following describes the derivative...Ch. 4.1 - Explain the relationship between the slope and the...Ch. 4.1 - Prob. 26ECh. 4.1 - Find each derivative. Dx9x-1/2+2x3/2Ch. 4.1 - Find each derivative. Dx8x4-3x3Ch. 4.1 - Prob. 29ECh. 4.1 - Find each derivative. f'3 if fx=x39-7x2Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - In Exercises 31-34, find the slope of the tangent...Ch. 4.1 - Prob. 35ECh. 4.1 - Find all points on the graph of fx=x3+9x2+19x-10...Ch. 4.1 - Prob. 37ECh. 4.1 - In Exercises 37-40, for each function find all...Ch. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - At what point on the graph of fx=-5x2+4x-2 is the...Ch. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - In Exercises 43-46 of section 1.4, the effect of a...Ch. 4.1 - Show that, for any constant k, ddxfxk=f'xk.Ch. 4.1 - Prob. 50ECh. 4.1 - Cancer Insulation workers who were exposed to...Ch. 4.1 - Prob. 52ECh. 4.1 - Insect Mating Patterns In an experiment testing...Ch. 4.1 - Prob. 54ECh. 4.1 - Bighorn Sheep The cumulative horn volume for...Ch. 4.1 - Brain Mass The brain mass of a human fetus during...Ch. 4.1 - Prob. 57ECh. 4.1 - Body Mass Index The body mass index BMI is a...Ch. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Dogs Human Age From the data printed in the...Ch. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Postal Rates U.S postal rates have steadily...Ch. 4.1 - Money The total amount of money in circulation for...Ch. 4.1 - Prob. 75ECh. 4.2 - YOUR TURN Find the derivative of y=x3+74-x2.Ch. 4.2 - Prob. 2YTCh. 4.2 - YOUR TURN Find Dx5x-32x+73x+7.Ch. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 26ECh. 4.2 - Use the quotient rule to find the derivative of...Ch. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Find the error in the following work....Ch. 4.2 - Prob. 32ECh. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Find an equation of the line tangent to the graph...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - For each function, find the values of x in which...Ch. 4.2 - Prob. 41ECh. 4.2 - Growth Models In Exercise 52 of section 1.5, the...Ch. 4.2 - Bacteria Population Assume that the total number...Ch. 4.2 - Work/Rest Cycles Murrells formula for calculating...Ch. 4.2 - Optimal Foraging Using data collected by zoologist...Ch. 4.2 - Cell Traction Force In a matrix of cells, the cell...Ch. 4.2 - Prob. 47ECh. 4.2 - Cellular Chemistry The release of a chemical...Ch. 4.2 - Prob. 49ECh. 4.2 - Memory Retention Some psychologists content that...Ch. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.3 - YOUR TURN For the functions in Example 1, find fg0...Ch. 4.3 - YOUR TURN Let fx=2x-3 and gx=x2+1. Find gfx.Ch. 4.3 - YOUR TURN Write hx=2x-33 as a composition of two...Ch. 4.3 - YOUR TURN Find dy/dx if y=5x2-6x-2.Ch. 4.3 - Prob. 5YTCh. 4.3 - Prob. 6YTCh. 4.3 - Prob. 7YTCh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - In Exercises 7-14, find f[gx] and g[fx]. fx=x+2;...Ch. 4.3 - In Exercises 7-14, find f[gx] and g[fx]....Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Write each function as the composition of two...Ch. 4.3 - Prob. 21ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 23ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Find the derivative of each function defined as...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Consider the following table of values of the...Ch. 4.3 - Prob. 45ECh. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - In Exercises 45-48, find the equation of the...Ch. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Katie and Sarah are working on taking the...Ch. 4.3 - Margy and Nate are working on taking the...Ch. 4.3 - Prob. 53ECh. 4.3 - Oil Pollution An oil well off the Gulf Coast is...Ch. 4.3 - African Wild Dog The African wild dog is currently...Ch. 4.3 - Thermal Inversion When there is a thermal...Ch. 4.3 - Prob. 57ECh. 4.3 - Calcium Usage To test an individuals use of...Ch. 4.3 - Drug Reaction The strength of a persons reaction...Ch. 4.3 - Extinction The probability of a population going...Ch. 4.3 - Candy The volume and surface area of a jawbreaker...Ch. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.4 - YOUR TURN 1 Find dy/dx for a. y=43x, b. y=e7x3+5Ch. 4.4 - Prob. 2YTCh. 4.4 - Prob. 3YTCh. 4.4 - YOUR TURN 4 The quantity in grams of a radioactive...Ch. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 25ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 31ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 33ECh. 4.4 - Find derivatives of the functions defined as...Ch. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Use graphical differentiation to verify that...Ch. 4.4 - Prob. 38ECh. 4.4 - Population Growth In section 2.1, Exercise 37, the...Ch. 4.4 - Minority Population In Section 2.1, Exercise 39,...Ch. 4.4 - Insect Growth The growth of a population of rare...Ch. 4.4 - Prob. 43ECh. 4.4 - Whooping Cranes Based on data from the U.S. Fish...Ch. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Mortality The percentage of people of any...Ch. 4.4 - Breast Cancer It has been observed that the...Ch. 4.4 - Arctic Foxes The age-weight relationship of female...Ch. 4.4 - Prob. 50ECh. 4.4 - Ayrshire Dairy Cattle The researchers from the...Ch. 4.4 - Cutlassfish The cutlassfish is one of the most...Ch. 4.4 - Prob. 53ECh. 4.4 - Dialysis One measure of whether a dialysis patient...Ch. 4.4 - Medical Literature It has been observed that there...Ch. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Radioactive Iron Researchers found that the...Ch. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Habit Strength According to work by the...Ch. 4.4 - Prob. 66ECh. 4.4 - Electricity In a series resistance-capacitance DC...Ch. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.5 - YOUR TURN Find the derivative of fx=log3x.Ch. 4.5 - Prob. 2YTCh. 4.5 - Prob. 3YTCh. 4.5 - Find the derivative of each function. y=ln8xCh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Find the derivative of each function. y=ln4x2-9xCh. 4.5 - Find the derivative of each function. y=ln-8x3+2xCh. 4.5 - Find the derivative of each function. y=lnx+5Ch. 4.5 - Prob. 8ECh. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Find the derivative of each function. y=xln2-x2Ch. 4.5 - Prob. 15ECh. 4.5 - Find the derivative of each function. v=lnuu3Ch. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Find the derivative of each function. y=3x2lnxCh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Find the derivative of each function. y=lnx-3Ch. 4.5 - Find the derivative of each function. y=lnlnxCh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Find the derivative of each function. py=lnyeyCh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Find the derivative of each function. y=log4x-3Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Find the derivative of each function. y=log74x-3Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Find the derivative of each function....Ch. 4.5 - Prob. 39ECh. 4.5 - Find the derivative of each function. z=10ylogyCh. 4.5 - Prob. 41ECh. 4.5 - Find the derivative of each function. fx=lnxex+2Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Use a graphing calculator to sketch the graph of...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - This exercise shows another way to derive the...Ch. 4.5 - Prob. 57ECh. 4.5 - Population Growth Suppose that the population of a...Ch. 4.5 - Body Surface Area There is a mathematical...Ch. 4.5 - Prob. 60ECh. 4.5 - Prob. 61ECh. 4.5 - Fruit Flies A study of the relation between the...Ch. 4.5 - Prob. 63ECh. 4.5 - Poverty The passage of the Social Security...Ch. 4.5 - Richter Scale The Richter scale provides a measure...Ch. 4.5 - Prob. 66ECh. 4.6 - YOUR TURN Find the derivative of y=5sin3x4.Ch. 4.6 - YOUR TURN Find the derivative of y=2sin3x.Ch. 4.6 - Prob. 3YTCh. 4.6 - Prob. 4YTCh. 4.6 - Prob. 5YTCh. 4.6 - Prob. 6YTCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 8ECh. 4.6 - Prob. 9ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 11ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 13ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 15ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 17ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 23ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 25ECh. 4.6 - Find the derivatives of the functions defined as...Ch. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Prob. 31ECh. 4.6 - In Exercises 27-32, recall that the slope of the...Ch. 4.6 - Find the derivative of cotx by using the quotient...Ch. 4.6 - Prob. 34ECh. 4.6 - Verify that the derivative of cscx is -cscxcotx....Ch. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Carbon Dioxide Levels At Barrow, Alaska,...Ch. 4.6 - Prob. 39ECh. 4.6 - Sound If a string with a fundamental frequency of...Ch. 4.6 - Prob. 41ECh. 4.6 - Revenue from Seasonal Merchandise The revenue...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 10CRCh. 4.CR - Determine whether each of the following statements...Ch. 4.CR - Prob. 12CRCh. 4.CR - Prob. 13CRCh. 4.CR - Prob. 14CRCh. 4.CR - Prob. 15CRCh. 4.CR - Prob. 16CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 19CRCh. 4.CR - Prob. 20CRCh. 4.CR - Prob. 21CRCh. 4.CR - Prob. 22CRCh. 4.CR - Prob. 23CRCh. 4.CR - Prob. 24CRCh. 4.CR - Prob. 25CRCh. 4.CR - Prob. 26CRCh. 4.CR - Prob. 27CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 29CRCh. 4.CR - Prob. 30CRCh. 4.CR - Prob. 31CRCh. 4.CR - Prob. 32CRCh. 4.CR - Prob. 33CRCh. 4.CR - Prob. 34CRCh. 4.CR - Prob. 35CRCh. 4.CR - Prob. 36CRCh. 4.CR - Prob. 37CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 39CRCh. 4.CR - Prob. 40CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 42CRCh. 4.CR - Prob. 43CRCh. 4.CR - Prob. 44CRCh. 4.CR - Prob. 45CRCh. 4.CR - Prob. 46CRCh. 4.CR - Prob. 47CRCh. 4.CR - Prob. 48CRCh. 4.CR - Prob. 49CRCh. 4.CR - Prob. 50CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 52CRCh. 4.CR - Prob. 53CRCh. 4.CR - Prob. 54CRCh. 4.CR - Prob. 55CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 57CRCh. 4.CR - Prob. 58CRCh. 4.CR - Prob. 59CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 61CRCh. 4.CR - Prob. 62CRCh. 4.CR - Prob. 63CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 65CRCh. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Use the rules for derivatives to find the...Ch. 4.CR - Prob. 68CRCh. 4.CR - Consider the following table of values of the...Ch. 4.CR - Consider the following table of values of the...Ch. 4.CR - Prob. 71CRCh. 4.CR - Prob. 72CRCh. 4.CR - Find the slope of the tangent line to the given...Ch. 4.CR - Prob. 74CRCh. 4.CR - Prob. 75CRCh. 4.CR - Prob. 76CRCh. 4.CR - Prob. 77CRCh. 4.CR - Prob. 78CRCh. 4.CR - Prob. 79CRCh. 4.CR - Prob. 80CRCh. 4.CR - Prob. 81CRCh. 4.CR - Prob. 82CRCh. 4.CR - Prob. 83CRCh. 4.CR - Prob. 84CRCh. 4.CR - Prob. 85CRCh. 4.CR - Prob. 86CRCh. 4.CR - Prob. 87CRCh. 4.CR - Prob. 88CRCh. 4.CR - Prob. 89CRCh. 4.CR - Exponential Growth Suppose a population is growing...Ch. 4.CR - Logistic Growth Suppose a population can be...Ch. 4.CR - Fish The length of the monkeyface prickleback, a...Ch. 4.CR - Prob. 93CRCh. 4.CR - Prob. 94CRCh. 4.CR - Prob. 95CRCh. 4.CR - Prob. 96CRCh. 4.CR - Prob. 97CRCh. 4.CR - Prob. 98CRCh. 4.CR - Prob. 99CRCh. 4.CR - Prob. 100CRCh. 4.CR - Prob. 101CRCh. 4.EA - Suppose that a particular plot of land can sustain...Ch. 4.EA - Prob. 2EA
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- Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.arrow_forwardEastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forwardGrowth Rate Versus Weight Ecologists have studied how a populations intrinsic exponential growth rate r is related to the body weight W for herbivorous mammals. In table 5.2, W is the adult weight measured in pounds, and r is growth rate per year. Animal Weight W r Short-tailed vole 0.07 4.56 Norway rat 0.7 3.91 Rue deer 55 0.23 White-tailed deer 165 0.55 American elk 595 0.27 African elephant 8160 0.06 Find a formula that models r as a power function of W, and draw a graph of this function.arrow_forward
- More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?arrow_forwardWhat is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?arrow_forward
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