A state game commission introduces 60 deer into newly acquired state game lands. The population N of the herd can be modeled by 10(6 + 2t) N = 1+ 0.05t where t is the time in years. Use differentials to approximate the change in the herd size from t = 4 to t = 5. (Round your answer to the nearest integer.) deer

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 state game commission introduces 60 deer into newly acquired state game lands. The population N of the herd can be modeled by
10(6 + 2t)
1 + 0.05t
N =
where t is the time in years. Use differentials to approximate the change in the herd size from t = 4 to t = 5. (Round your answer to the nearest integer.)
deer
Transcribed Image Text:A state game commission introduces 60 deer into newly acquired state game lands. The population N of the herd can be modeled by 10(6 + 2t) 1 + 0.05t N = where t is the time in years. Use differentials to approximate the change in the herd size from t = 4 to t = 5. (Round your answer to the nearest integer.) deer
Expert Solution
Step 1

Given that N=106+2t1+0.05t.

Differentiate N=106+2t1+0.05t with respect to t, we get

dNdt=ddt106+2t1+0.05t=10ddt6+2t1+0.05t=101+0.05tddt6+2t6+2tddt1+0.05t1+0.05t2=101+0.05t0+216+2t0+0.0511+0.05t2=1021+0.05t0.056+2t1+0.05t2=102+0.1t0.30.1t1+0.05t2=1020.31+0.05t2=101.71+0.05t2=171+0.05t2

Hence, dNdt=171+0.05t2.

Hence, dN=171+0.05t2dt.

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