Starting with an initial value of P(0)= 75, the population of a prairie dog community grows at a rate ofP'(t) = 10 -(in units of prairie dogs/month), for 0sts 50.a. What is the population 14 months later?b. Find the population P(t) for 0sts 50.a. After 14 months, the population is(Type a whole number. Round to the nearest prairie dog as needed.)prairie dogs.

The growth rate of population of prairie dog community is P'(t)=10-t5 given that, P(0)=75 a) we…

tarting with an initial value of P(0)= 75, the population (t) = 10 (in units of prairie dogs/month), for 0sts %3D What is the population 14 months later? . Find the population P(t) for 0sts 50. . After 14 months, the population is prairie dogs. Tyne a whole number. Round to the nearest prairie dog

tarting with an initial value of P(0)= 75, the population (t) = 10 (in units of prairie dogs/month), for 0sts %3D What is the population 14 months later? . Find the population P(t) for 0sts 50. . After 14 months, the population is prairie dogs. Tyne a whole number. Round to the nearest prairie dog

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Question

Starting with an initial value of P(0)= 75, the population of a prairie dog community grows at a rate of
P'(t) = 10 -
(in units of prairie dogs/month), for 0sts 50.
a. What is the population 14 months later?
b. Find the population P(t) for 0sts 50.
a. After 14 months, the population is
(Type a whole number. Round to the nearest prairie dog as needed.)
prairie dogs.

Expert Solution

Step 1

The growth rate of population of prairie dog community is

$P' (t) = 10 - \frac{t}{5}$

given that,

P(0)=75

a) we have to find population 14 month late

b) find the population P(t) for $0 \leq t \leq 50$

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