Need help exponential decay problem?
Hi, everyone, I know the concept of the exponential decay problem, but for some reason, I cannot get this answer and therefore, the answer in the back of the book is not correct.
Q. The value of a car after it is purchased depreciates according to the formula V(n)=25,000(0.85)^n, where V(n) is the car’s value in the nth year after it was purchased.
a) What is the car’s value at the end of 3 years
b) How much value does the car lose in its first year?
c) How much value does it lose in its fifth year
d) After how many years will the value of the car be half of the original purchase price?
Please help me out and I am greatly appreciates.
I was wondering what is log means?
a)
V(3) = 25000 * (0.85)^3 = 15353.13
b)
It loses 100-85 = 15% of its value.
25000 * 0.15 = 3750
c)
Determine the value after the fourth year and then find out what 15% of that value are.
in short:
( 25000 * 0.85^4 ) * 0.15 = 1957.52
d)
25000 / 2 = 12500
12500 = 25000 * 0.85^n
12500 / 25000 = 0.85^n
0.5 = 0.85^n
log 0.5 = n * log 0.85
log 0.5 / log 0.85 = n
4.265… = n
the car will be worth 50% of its original value after a little more than 4 years.
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