A new car is purchased for $45,000. During the next 5 years, the rate of change in the value of the car is given by the differential equation dx/dt = -kx, where $x is the value of the car after t years, and k is a constant. After 5 years, the car is expected to have a value of $15,000. Find the value of the car when it is 3 years old.

Question

anonymous · Answer

Solve the general ODE and get y=Ce^kt. Plug in 5 years and 15,000 to solve for the constant of integration, then plug in the 3 years and solve.

anonymous · Answer

if you don't mind me saying, this is a really dumb way dx/dt blah blah to solve this question.  you know that in 5 years it will be worth 1/3 of its current value, so all you need to do is plug in 3 into the easy formula 
$$45\times (\frac{1}{3})^{\frac{t}{5}}$$

anonymous · Answer

in thousands of course.  just compute 
$$45(\frac{1}{3})^{\frac{2}{3}}$$ and be done