model for the population P(t) in a suburb of a large city is given by the initial-value problem dP P(10-1 - 10-7P). P(0) = 6000, dt ere t is measured in months. d the population P of the suburb at time t. =) = mat is the limiting value of the population? what time will the population be equal to one- of this limiting value? (Round your answer to one decimal place.) months

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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A model for the population P(t) in a suburb of a large city is given by the initial-value problem
dP
P(10-1- 10-7P),
P(0) = 6000,
dt
where t is measured in months.
Find the population P of the suburb at time t.
P(t) =
What is the limiting value of the population?
At what time will the population be equal to one-half of this limiting value? (Round your answer to one decimal place.)
months
Transcribed Image Text:A model for the population P(t) in a suburb of a large city is given by the initial-value problem dP P(10-1- 10-7P), P(0) = 6000, dt where t is measured in months. Find the population P of the suburb at time t. P(t) = What is the limiting value of the population? At what time will the population be equal to one-half of this limiting value? (Round your answer to one decimal place.) months
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