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40-43. Population growth 40. Starting with an initial value of P(0) = 55, the population of a prairie dog community grows at a rate of P' (t) = 20 – t/5 (prairie dogs/month), for 0 < t s 200, where t is measured in months. a. What is the population 6 months later? b. Find the population P(t), for 0 s t s 200. 41. When records were first kept (t = 0), the population of a rural town was 250 people. During the following years, the population grew at a rate of P'(t) = 30(1 + Vĩ), where t is measured in years. a. What is the population after 20 years? b. Find the population P(t) at any time t 0. 42. The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35 foxes. The growth rate in units of foxes/year was observed to be P'(t) = 5 + 10 sin ". a. What is the population 15 years later? 35 years later? b. Find the population P(t) at any time t z 0.

40-43. Population growth 40. Starting with an initial value of P(0) = 55, the population of a prairie dog community grows at a rate of P' (t) = 20 – t/5 (prairie dogs/month), for 0 < t s 200, where t is measured in months. a. What is the population 6 months later? b. Find the population P(t), for 0 s t s 200. 41. When records were first kept (t = 0), the population of a rural town was 250 people. During the following years, the population grew at a rate of P'(t) = 30(1 + Vĩ), where t is measured in years. a. What is the population after 20 years? b. Find the population P(t) at any time t 0. 42. The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35 foxes. The growth rate in units of foxes/year was observed to be P'(t) = 5 + 10 sin ". a. What is the population 15 years later? 35 years later? b. Find the population P(t) at any time t z 0.

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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40-43. Population growth 40. Starting with an initial value of P(0) = 55, the population of a prairie dog community grows at a rate of P' (t) = 20 – t/5 (prairie dogs/month), for 0 < t s 200, where t is measured in months. a. What is the population 6 months later? b. Find the population P(t), for 0 s t s 200. 41. When records were first kept (t = 0), the population of a rural town was 250 people. During the following years, the population grew at a rate of P'(t) = 30(1 + Vĩ), where t is measured in years. a. What is the population after 20 years? b. Find the population P(t) at any time t 0. 42. The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35 foxes. The growth rate in units of foxes/year was observed to be P'(t) = 5 + 10 sin ". a. What is the population 15 years later? 35 years later? b. Find the population P(t) at any time t z 0.
Transcribed Image Text:40-43. Population growth 40. Starting with an initial value of P(0) = 55, the population of a prairie dog community grows at a rate of P' (t) = 20 – t/5 (prairie dogs/month), for 0 < t s 200, where t is measured in months. a. What is the population 6 months later? b. Find the population P(t), for 0 s t s 200. 41. When records were first kept (t = 0), the population of a rural town was 250 people. During the following years, the population grew at a rate of P'(t) = 30(1 + Vĩ), where t is measured in years. a. What is the population after 20 years? b. Find the population P(t) at any time t 0. 42. The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t = 0), the population was 35 foxes. The growth rate in units of foxes/year was observed to be P'(t) = 5 + 10 sin ". a. What is the population 15 years later? 35 years later? b. Find the population P(t) at any time t z 0.
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