Answer to Question #201467 in Calculus for raf

Question #201467

welch construction has found that the value of the company tractor is decreasing at a rate give by v(t)= -390te-0.012t^2, where t represents the number of years after purchase. if the company purchased the tractor for $17650, what is the value of the tractor 3 years after purchase


1
Expert's answer
2021-06-07T14:14:40-0400

Answer:-


U(t)=v(t)dt=390te0.012t2dtU(t)=\int v(t)dt=\int-390te^{-0.012t^2}dt=16250e0.012t2+C=-16250e^{-0.012t^2}+C

Given U(0)=17650U(0)=17650



17650=16250+C=>C=3390017650=-16250+C=>C=33900U(t)=16250e0.012t2+33900U(t)=-16250e^{-0.012t^2}+33900U(3)=16250e0.012(3)2+33900U(3)=-16250e^{-0.012(3)^2}+33900U(3)=$19313.55U(3)=\$19313.55

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