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65. Population growth. Before 1859, rabbits did not exist in Australia. That year, a settler released 24 rabbits into the wild. Without natural predators, the growth of the Australian rabbit population can be modeled by the un- inhibited growth model dP/dt = kP, where P(t) is the population of rabbits t years after 1859. (Source: www dpi.vic.gov.au/agriculture.) a) When the rabbit population was estimated to be 8900, its rate of growth was about 2630 rabbits per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the rabbit population in 1900 (t = 41) and the rate at which it was increasing in that year. c) Without using a calculator, find P'(41)/P(41).

65. Population growth. Before 1859, rabbits did not exist in Australia. That year, a settler released 24 rabbits into the wild. Without natural predators, the growth of the Australian rabbit population can be modeled by the un- inhibited growth model dP/dt = kP, where P(t) is the population of rabbits t years after 1859. (Source: www dpi.vic.gov.au/agriculture.) a) When the rabbit population was estimated to be 8900, its rate of growth was about 2630 rabbits per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the rabbit population in 1900 (t = 41) and the rate at which it was increasing in that year. c) Without using a calculator, find P'(41)/P(41).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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65. Population growth. Before 1859, rabbits did not exist in Australia. That year, a settler released 24 rabbits into the wild. Without natural predators, the growth of the Australian rabbit population can be modeled by the un- inhibited growth model dP/dt = kP, where P(t) is the population of rabbits t years after 1859. (Source: www dpi.vic.gov.au/agriculture.) a) When the rabbit population was estimated to be 8900, its rate of growth was about 2630 rabbits per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the rabbit population in 1900 (t = 41) and the rate at which it was increasing in that year. c) Without using a calculator, find P'(41)/P(41).
Transcribed Image Text:65. Population growth. Before 1859, rabbits did not exist in Australia. That year, a settler released 24 rabbits into the wild. Without natural predators, the growth of the Australian rabbit population can be modeled by the un- inhibited growth model dP/dt = kP, where P(t) is the population of rabbits t years after 1859. (Source: www dpi.vic.gov.au/agriculture.) a) When the rabbit population was estimated to be 8900, its rate of growth was about 2630 rabbits per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the rabbit population in 1900 (t = 41) and the rate at which it was increasing in that year. c) Without using a calculator, find P'(41)/P(41).
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