calculus
posted by steve alexander on .
An automobile with seven years of use has a commercial value of $34057.7, but five years ago its value was $72250. If the value of such automobile varies exponentially with the time. (3641)
36. What was the value of the automobile when it was new?
37. What will be the value of the automobile after 10 years of use?
38. How many years of use will the automobile have with a value of $10277?
39. After how long of use does the value of the automobile reduce to the half?
40. After how many years of use the value of the automobile reduces to the fourth part of its initial value?
41. After how many years of use does the value of the automobile reduce to the third part of its initial velocity?

the general equation would be
value = a(e)^(kt) where a is the initital vaue, and k is a constant
you end up with 2 equations:
34057.7 = a(e)^(7k)  equation #1
72250 = a(e)^(5k)  eqution #2
I divided #1 by #2 to get .4713865 = e^2k
and got k = .37604 using logs
put that back into #2 I got a = 473581
(a very unreasonable price for an automobile, but then again after 5 years it was still worth $72,000)
so now we have
Value = 473581(e)^.37604t
and you can find any of the other answers quite easily.