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 5800, 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). 5800 P(t) = 1+4.80 e -0.5t a) Find the population after 7 years. 5066 (Round to the nearest integer as needed) b) Find the rate of change, P'(t). OA. 27,840.00 -0.5t OB. 13,920.00 e -0 5t (1+ 5800 e -0.5t) 2 (1+4 80 e -0 51)? OC. (1+4 80 e -05t)2 OD. 27,840.00 -0.5t 13,920.00 e -0.5t (1+4.80 e 051)?
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 5800, 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). 5800 P(t) = 1+4.80 e -0.5t a) Find the population after 7 years. 5066 (Round to the nearest integer as needed) b) Find the rate of change, P'(t). OA. 27,840.00 -0.5t OB. 13,920.00 e -0 5t (1+ 5800 e -0.5t) 2 (1+4 80 e -0 51)? OC. (1+4 80 e -05t)2 OD. 27,840.00 -0.5t 13,920.00 e -0.5t (1+4.80 e 051)?
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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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 5800, 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).
5800
P(t) =
1+4.80 e -0.5t
a) Find the population after 7 years.
5066 (Round to the nearest integer as needed.)
b) Find the rate of change, P'(t).
O A.
27,840.00-0.5t
(1+5800 e -051)2
OC. (1+4 80 e -0,51)²
OB.
13,920.00 e -0.5t
- 0.5t) 2
(1+4.80 e ~0 5')²
OD.
27,840.00 -0.5t
13,920.00 e -0.5t
+ 4.80 e -0 51)²
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