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0s15 20, where i is the number of years after the base year of 1905. 20. During the time period 1905-1920, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. This, in turn, resulted in a rapid increase in the deer popu- lation P(t), until food supplies were exhausted and famine led to a steep decline in P(t). A study of this ecological disaster determined that during the time period 1905–1920, the rate of change of the popula- tion, P'(t), could be modeled by the function a. In what year during this period was the deer population the largest? b. In what year did the rate of growth P'(t) begin to decline? P() = (100 – 50)

0s15 20, where i is the number of years after the base year of 1905. 20. During the time period 1905-1920, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. This, in turn, resulted in a rapid increase in the deer popu- lation P(t), until food supplies were exhausted and famine led to a steep decline in P(t). A study of this ecological disaster determined that during the time period 1905–1920, the rate of change of the popula- tion, P'(t), could be modeled by the function a. In what year during this period was the deer population the largest? b. In what year did the rate of growth P'(t) begin to decline? P() = (100 – 50)

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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344 Chapter 4 Applications of Differentiation 0<ts 20, where t is the number of years after the base year of 1905. 20. During the time period 1905–1920, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. This, in turn, resulted in a rapid increase in the deer popu- lation P(t), until food supplies were exhausted and famine led to a steep decline in P(t). A study of this ecological disaster determined that during the time period 1905–1920, the rate of change of the popula- tion, P'(t), could be modeled by the function a. In what year during this period was the deer population the largest? b. In what year did the rate of growth P'(t) begin to decline? P(t) = 1 (100 – 5t)t³ GROUP PROJECTS Seeing a project through on your own, or working in a small group to complete a project, teaches important skills. The following projects provide opportunities to develop such skills. Project 4A Optimal swimming patterns In getting from one spot to another, fish have to con- tend with drag forces and gravity. Drag forces are much greater when a fish is swimming than when it is merely gliding. To reduce the amount of time spent swimming, fish that are heavier than water engage in burst swim- ming in which they alternate between gliding and swim- ming upward. This burst swimming leads to a vertical zigzag motion of the fish in the water as shown below: • The drag on the gliding fish is D and the drag on the swimming fish is kD where k > 1. • The fish has sufficient top/bottom surface area (e.g., a skate) that frictional forces perpendicular to the top/bottom of the fish cancel the component of the gravitational force that is perpendicular to the top/bottom of the fish. • The energy expended by the fish in swimming is pro- portional to the force it exerts in moving. Under these assumptions, your project should do the following: a
Transcribed Image Text:344 Chapter 4 Applications of Differentiation 0<ts 20, where t is the number of years after the base year of 1905. 20. During the time period 1905–1920, hunters virtually wiped out all large predators on the Kaibab Plateau near the Grand Canyon in northern Arizona. This, in turn, resulted in a rapid increase in the deer popu- lation P(t), until food supplies were exhausted and famine led to a steep decline in P(t). A study of this ecological disaster determined that during the time period 1905–1920, the rate of change of the popula- tion, P'(t), could be modeled by the function a. In what year during this period was the deer population the largest? b. In what year did the rate of growth P'(t) begin to decline? P(t) = 1 (100 – 5t)t³ GROUP PROJECTS Seeing a project through on your own, or working in a small group to complete a project, teaches important skills. The following projects provide opportunities to develop such skills. Project 4A Optimal swimming patterns In getting from one spot to another, fish have to con- tend with drag forces and gravity. Drag forces are much greater when a fish is swimming than when it is merely gliding. To reduce the amount of time spent swimming, fish that are heavier than water engage in burst swim- ming in which they alternate between gliding and swim- ming upward. This burst swimming leads to a vertical zigzag motion of the fish in the water as shown below: • The drag on the gliding fish is D and the drag on the swimming fish is kD where k > 1. • The fish has sufficient top/bottom surface area (e.g., a skate) that frictional forces perpendicular to the top/bottom of the fish cancel the component of the gravitational force that is perpendicular to the top/bottom of the fish. • The energy expended by the fish in swimming is pro- portional to the force it exerts in moving. Under these assumptions, your project should do the following: a
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