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66. Population growth. Suppose 30 sparrows are released into a region where they have no natural predators. The growth of the region's sparrow population can be modeled by the uninhibited growth model dP/dt = kP, where P(t) is the population of sparrows t years after their initial release. a) When the sparrow population is estimated at 12,500, its rate of growth is about 1325 sparrows per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the number of sparrows after 70 yr. c) Without using a calculator, find P'(70)/P(70).

66. Population growth. Suppose 30 sparrows are released into a region where they have no natural predators. The growth of the region's sparrow population can be modeled by the uninhibited growth model dP/dt = kP, where P(t) is the population of sparrows t years after their initial release. a) When the sparrow population is estimated at 12,500, its rate of growth is about 1325 sparrows per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the number of sparrows after 70 yr. c) Without using a calculator, find P'(70)/P(70).

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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66. Population growth. Suppose 30 sparrows are released into a region where they have no natural predators. The growth of the region's sparrow population can be modeled by the uninhibited growth model dP/dt = kP, where P(t) is the population of sparrows t years after their initial release. a) When the sparrow population is estimated at 12,500, its rate of growth is about 1325 sparrows per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the number of sparrows after 70 yr. c) Without using a calculator, find P'(70)/P(70).
Transcribed Image Text:66. Population growth. Suppose 30 sparrows are released into a region where they have no natural predators. The growth of the region's sparrow population can be modeled by the uninhibited growth model dP/dt = kP, where P(t) is the population of sparrows t years after their initial release. a) When the sparrow population is estimated at 12,500, its rate of growth is about 1325 sparrows per year. Use this information to find k, and then find the particular solution of the differential equation. b) Find the number of sparrows after 70 yr. c) Without using a calculator, find P'(70)/P(70).
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