Asked by Jayme
An car was purchased for $47000 and its depreciation value is 22% each year.
How long would it take the car to be worth nothing (zero dollars)?
Explain.
How long would it take the car to be worth nothing (zero dollars)?
Explain.
Answers
Answered by
Reiny
since it decreases by 22% each year, 78% of the previous years value will be maintained.
so you have
Value = 47000(.78)^n where n is the number of years.
so for the value to be zero dollars, we could set Value = 0 and solve for n
this causes a problem, since to solve
0 = 47000(.78)^n
n = log 0/log.78 , but log 0 is undefined, implying that n would be infinitely large
this makes sense, since as long as I have any amount left, 78% of it will still be some value
If I decide that a value of 49 cents is less than a Dollar, if we round to the nearest dollar, I get
.49 = 47000(.78)^n
I get n = appr. 46 years.
so you have
Value = 47000(.78)^n where n is the number of years.
so for the value to be zero dollars, we could set Value = 0 and solve for n
this causes a problem, since to solve
0 = 47000(.78)^n
n = log 0/log.78 , but log 0 is undefined, implying that n would be infinitely large
this makes sense, since as long as I have any amount left, 78% of it will still be some value
If I decide that a value of 49 cents is less than a Dollar, if we round to the nearest dollar, I get
.49 = 47000(.78)^n
I get n = appr. 46 years.