In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by P(t) 2000 1+e5.3-0.4t with t measured in years since 1774. Using a calculator or computer: a. Graph P. Does the population level off? b. Estimate when the rabbit population grew most rapidly. How large was the population at that time? c. Find the inflection point on the graph and explain its significance for the rabbit population. d. What natural causes could lead to the shape of the graph of P?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 33PT: Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine...
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In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by
2000
1+e5.3-0.4t
P(t)
with t measured in years since 1774. Using a calculator or computer:
a. Graph P. Does the population level off?
b. Estimate when the rabbit population grew most rapidly. How large was the population at that time?
c. Find the inflection point on the graph and explain its significance for the rabbit population.
d. What natural causes could lead to the shape of the graph of P?
Transcribed Image Text:In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by 2000 1+e5.3-0.4t P(t) with t measured in years since 1774. Using a calculator or computer: a. Graph P. Does the population level off? b. Estimate when the rabbit population grew most rapidly. How large was the population at that time? c. Find the inflection point on the graph and explain its significance for the rabbit population. d. What natural causes could lead to the shape of the graph of P?
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