Posted by **steve alexander** on Tuesday, November 25, 2008 at 8:41pm.

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 -
**Reiny**, Tuesday, November 25, 2008 at 10:35pm
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.

## Answer this Question

## Related Questions

- calculus - X. An automobile with seven years of use has a commercial value of $...
- Math(Please check) - The value of an automobile was $15,780 in 1994 and ...
- ALG 2/Trig - A new $12,000 automobile decreases in value every year. What is it'...
- Calculus - The median value of a home in a particular market is decreasing ...
- College Algebra - Value of Computer Software The value V, in dollars, of a ...
- interest - an inheritance will be 20000. the interest rate for the the time ...
- Calculus - I am confused on how to solve this problem : $5000 is invested for 4 ...
- finance - A 5-year annuity of ten $4500 semiannual payments will begin 9 years ...
- finance - Can someone please help me with the following question. I am not sure ...
- math - The value of a new car decreases exponentially.Suppose your mother buys a...