Concept explainers
Graphing Logistic Growth Functions Use a graphing utility to graph the function. Describe the shape of the graph for very large and very small values of x.
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Chapter 4 Solutions
WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term
- Whooping Cranes Based on data from the U.S. Fish and Wildlife Service, the population of whooping cranes in the Aransas-Wood Buffalo National Park can be approximated by a logistic function with k=6.0110-5, with a population in 1958 of 32 and a maximum population of 787. Source: U.S. Fish and Wildlife Service. a. Find the growth function Gt for the whooping crane population, where t is the time since 1938, when the park first started counting the cranes. b. Find the initial population G0. Find the population and rate of growth in the following years. c. 1945 d. 1985 e. 2005 f. What happens to the rate of growth over time?arrow_forwardSales 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_forwardModeling 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?arrow_forward
- Tracer Dye The amount of a tracer dye injected into the blood stream decrease exponentially, with a decay constant of 3 per minute. If 6 cc are present initially, how many cubic centimeters are present after 10 minutes? Here k will be negative.arrow_forwardWhat is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?arrow_forwardExponential Growth Is the graph of exponential growth versus time increasing or decreasing?arrow_forward
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