# calculus

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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. (36-41)
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?

• calculus -

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.

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