I Graphing Exponential and Logarithmic FunctionsSketch the graph of the function. State the domain, range, andasymptote.5. f(x) = 3-26. f(x) = 2-*+18. g(x) = 5-* – 510. G(x) = -e*+1 – 27. g(x) = 3 + 2*9. F(x) = e-1 + 1

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Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.2: The Natural Exponential Function

Problem 12E

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Reaction Time For certain decisions, the time it takes to respond is a logarithmic function of the number of choices faced. One model is, R=0.17+0.44logN where R is the reaction time in seconds and N is the number of choices. a.Draw a graph of R versus N. Include values of N from 1 to 10 choices. b.Using functional notation, express the reaction if there are seven choices, and then calculate that time. c.If the reaction is to be at most 0.5 second, how many choices can there be? d.If the number of choices increases by a factor of 10, what happens to the reaction time. e.Explain in practical terms what the concavity of graph means.
A Population of Foxes A breeding group of foxes is introduced into a protected area, and the population growth follws a logistic pattern. After t years, the population of foxes is given by N=37.50.25+0.76t foxes. a. How many foxes were intorduced into the protected area? b. Make a graph of N versus t and explain in words how the populatoin of foxes increases with time. c. When will the fox population reach 100 individuals?
Radioactive Decay The half-life of radium-226 is 1590 years. a If a sample has a mass of 150 mg, find a function that models the mass that remains after t years. b Find the mass that will remain after 1000 years. c After how many years will only 50 mg remain?
Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?
Exponential Function from a Graph Find the exponential function f(x)=ax whose graph is given.
Newton’s Law ofCooling states that the temperatureTof an object at any time t can be described by theequation T=Ts+(T0Ts)ekt, where Ts is thetemperature of the surrounding environment, T0 is the initial temperature of the object, and k is thecooling rate. Use the definition of a logarithm alongwith properties of logarithms to solve the formula fortime tsuch that tis equal to a single logarithm.
Radioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg, find a function that models the mass that remains after tyears. (b)Find the mass that will remain after 1000 years. (c)After how many years will only 50 mg remain?

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I Graphing Exponential and Logarithmic Functions Sketch the graph of the function. State the domain, range, and asymptote. 5. f(x) = 3-2 6. f(x) = 2-*+1 8. g(x) = 5-* – 5 10. G(x) = -e*+1 – 2 7. g(x) = 3 + 2* 9. F(x) = e-1 + 1

I Graphing Exponential and Logarithmic Functions Sketch the graph of the function. State the domain, range, and asymptote. 5. f(x) = 3-2 6. f(x) = 2-+1 8. g(x) = 5- – 5 10. G(x) = -e+1 – 2 7. g(x) = 3 + 2 9. F(x) = e-1 + 1