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.

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.

To determine how long it would take for the car to be worth nothing, we need to calculate the number of years it would take for the depreciation value to accumulate to the original purchase price of $47,000.

The depreciation value of 22% each year means that the car loses 22% of its value annually. To calculate this, we can use the formula:

Depreciation value = Original value * (Depreciation rate / 100)

In this case, the depreciation value would be calculated as:

Depreciation value = $47,000 * (22% / 100)
= $47,000 * 0.22
= $10,340

So, each year, the car loses $10,340 in value.

To calculate the number of years it would take for the car to be worth nothing, we can divide the original purchase price of $47,000 by the depreciation value:

Number of years = Original purchase price / Depreciation value
= $47,000 / $10,340
= 4.54 years (approximately)

Therefore, the car would take approximately 4.54 years to be worth nothing (zero dollars).