The value of a computer t years after purchase is v(t)=2000e^-.35t dollars. At what rate is the computer value falling after three years?

Question

anonymous · Answer

I don't know how I would go about solving. I got: v(3)=2000e^-1.05

campbell_st · Answer

find the 1st derivative of the function then substitute t = 3 to find the rate of depreciation.

anonymous · Answer

ok. thanks. for the first derivative I got -700e^-3.5t

campbell_st · Answer

thats it... and then substitute x = 3

the 1st derivative gives the equation of the slope... or the equation of the rate of change...

and you are looking at the change in value over time....

anonymous · Answer

so you would get -700e^-1.05. I guess I am stuck at this part. Do I multiply the -700 by -1.05?

campbell_st · Answer

nope you need a calculator and evaluate 

$$-700 \times e^{-1.05}... or.... \frac{700}{e^{1.05}}$$

anonymous · Answer

alrighty. Thanks so much!!! I think I got it. 244.96

campbell_st · Answer

so it has lost $244.96 in value in the 3rd year

anonymous · Answer

Thanks again! :)