A population is modeled by a function P that satisfies the differential equation dP = k(1200 – P), where t is time in years andk is the constant of proportionality. dt When t = 0, the population is 300, P(0) = 300. (a) Find P(t) in terms of t and k. (b) If P(4) = 600, find the value of k. (c) Find lim P(t)..
A population is modeled by a function P that satisfies the differential equation dP = k(1200 – P), where t is time in years andk is the constant of proportionality. dt When t = 0, the population is 300, P(0) = 300. (a) Find P(t) in terms of t and k. (b) If P(4) = 600, find the value of k. (c) Find lim P(t)..
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 population is modeled by a function P that satisfies the differential equation
dP
=k(1200 – P), where t is time in years and k is the constant of proportionality.
dt
When t = 0, the population is 300, P(0) = 300.
(a) Find P(t) in terms of t and k.
(b) If P(4) = 600, find the value of k.
(c) Find lim P(t)..
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