In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by 2000 P(t) = 1+ e5.3–0,4t with t measured in years since 1774. Use a calculator or computer to answer the following questions. (a) Graph P. Does the population level off? If it does, at what population? If it does not, enter NA. The population levels off at about rabbits. (b) Estimate when the rabbit population grew most rapidly. How large was the population at that time? Round the number of years to the nearest integer. The rabbit population grew most rapidly approximately i years after Captain Cook left the rabbits on the island, when the population was rabbits. (c) Find the inflection point on the graph and explain its significance for the rabbit population. Round your answer to the nearest integer.
In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by 2000 P(t) = 1+ e5.3–0,4t with t measured in years since 1774. Use a calculator or computer to answer the following questions. (a) Graph P. Does the population level off? If it does, at what population? If it does not, enter NA. The population levels off at about rabbits. (b) Estimate when the rabbit population grew most rapidly. How large was the population at that time? Round the number of years to the nearest integer. The rabbit population grew most rapidly approximately i years after Captain Cook left the rabbits on the island, when the population was rabbits. (c) Find the inflection point on the graph and explain its significance for the rabbit population. Round your answer to the nearest integer.
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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![In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by
\[
P(t) = \frac{2000}{1 + e^{5.3 - 0.4t}}
\]
with \( t \) measured in years since 1774. Use a calculator or computer to answer the following questions.
(a) **Graph \( P \):** Does the population level off? If it does, at what population? If it does not, enter NA.
The population levels off at about [ ] rabbits.
(b) **Estimate when the rabbit population grew most rapidly.** How large was the population at that time?
Round the number of years to the nearest integer.
The rabbit population grew most rapidly approximately [ ] years after Captain Cook left the rabbits on the island, when the population was [ ] rabbits.
(c) **Find the inflection point on the graph and explain its significance for the rabbit population.**
Round your answer to the nearest integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca5e629a-9287-4ec7-9b80-8449992c5732%2F746ad5b9-2153-4da5-b1c0-922e478dc295%2Fu63fbcw_processed.png&w=3840&q=75)
Transcribed Image Text:In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by
\[
P(t) = \frac{2000}{1 + e^{5.3 - 0.4t}}
\]
with \( t \) measured in years since 1774. Use a calculator or computer to answer the following questions.
(a) **Graph \( P \):** Does the population level off? If it does, at what population? If it does not, enter NA.
The population levels off at about [ ] rabbits.
(b) **Estimate when the rabbit population grew most rapidly.** How large was the population at that time?
Round the number of years to the nearest integer.
The rabbit population grew most rapidly approximately [ ] years after Captain Cook left the rabbits on the island, when the population was [ ] rabbits.
(c) **Find the inflection point on the graph and explain its significance for the rabbit population.**
Round your answer to the nearest integer.
![(c) Find the inflection point on the graph and explain its significance for the rabbit population.
Round your answer to the nearest integer.
The inflection point is approximately [text box] years after Captain Cook left the rabbits on the island which coincides with the population [dropdown menu].
(d) What natural causes could lead to the shape of the graph of P?
The shape of the graph could be caused by [dropdown menu].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca5e629a-9287-4ec7-9b80-8449992c5732%2F746ad5b9-2153-4da5-b1c0-922e478dc295%2F0zshwbq_processed.png&w=3840&q=75)
Transcribed Image Text:(c) Find the inflection point on the graph and explain its significance for the rabbit population.
Round your answer to the nearest integer.
The inflection point is approximately [text box] years after Captain Cook left the rabbits on the island which coincides with the population [dropdown menu].
(d) What natural causes could lead to the shape of the graph of P?
The shape of the graph could be caused by [dropdown menu].
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