Question

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

Answer 1

$$U(t)=\int v(t)dt=\int-390te^{-0.012t^2}dt$$

$$=-16250e^{-0.012t^2}+C$$

Given $U(0)=17650$

$$17650=-16250+C=>C=33900$$

$$U(t)=-16250e^{-0.012t^2}+33900$$

$$U(3)=-16250e^{-0.012(3)^2}+33900$$

$$U(3)=\$19313.55$$