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A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict Uthe population to a limiting value of 5780, to which the population gets closer and closer but which it never reaches. The population of the island after time t, in years, is approximated by the logistic equation given below. Complete parts (a) through (c). 5780 P()= 1+4.78e 05 a) Find the population after 10 years. 1 (Round to the nearest integer as needed. )

A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict Uthe population to a limiting value of 5780, to which the population gets closer and closer but which it never reaches. The population of the island after time t, in years, is approximated by the logistic equation given below. Complete parts (a) through (c). 5780 P()= 1+4.78e 05 a) Find the population after 10 years. 1 (Round to the nearest integer as needed. )

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 9CC
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b) Find the rate of change, P'(t). OA. -0.5t 27,628.40 OB. 13,814.20 e -0.5t (1+5780 e -0.5t) 2 (1+4.78 e -0.5t) 2 Oc. 27,628.40 -0.5t OD. (1+4.78 e -0.5t) 2 (1+4.78 e -0.5t) 2 13,814.20 e -0.5t c) Sketch a graph of the function. Choose the correct graph below. OA. OB. Oc. OD. AP() 6000- AP() 6000- AP() 6000 AP() 6000- 20 O Time Remaining: 00:5
Transcribed Image Text:b) Find the rate of change, P'(t). OA. -0.5t 27,628.40 OB. 13,814.20 e -0.5t (1+5780 e -0.5t) 2 (1+4.78 e -0.5t) 2 Oc. 27,628.40 -0.5t OD. (1+4.78 e -0.5t) 2 (1+4.78 e -0.5t) 2 13,814.20 e -0.5t c) Sketch a graph of the function. Choose the correct graph below. OA. OB. Oc. OD. AP() 6000- AP() 6000- AP() 6000 AP() 6000- 20 O Time Remaining: 00:5
A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict the population to a limiting value of 5780, to which the population gets closer and closer but which it never reaches. The population of the island after time t, in years, is approximated by the logistic equation given below. Complete parts (a) through (c). 5780 P(1) = 1+4.78e -0.51 a) Find the population after 10 years. 1 (Round to the nearest integer as needed.) b) Find the rate of change. P'(t).
Transcribed Image Text:A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never rescued. The natural resources of the island restrict the population to a limiting value of 5780, to which the population gets closer and closer but which it never reaches. The population of the island after time t, in years, is approximated by the logistic equation given below. Complete parts (a) through (c). 5780 P(1) = 1+4.78e -0.51 a) Find the population after 10 years. 1 (Round to the nearest integer as needed.) b) Find the rate of change. P'(t).
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