Question A new car is purchased for 20700 dollars. The value of the car depreciates at 8% per year. To the nearest year, how long will it be until the value of the car is 7200 dollars? Answer Attemptiontofy

## Step 1
The problem involves the concept of depreciation, which is a common topic in financial mathematics. The car's value decreases by 8% each year, which means it retains 92% of its value each year. This is because 100% - 8% = 92%.

## Step 2
We need to find out how many years it will take for the car's value to depreciate from $$20700 to$$ 7200. We can use the formula for exponential decay to solve this problem.

### The formula for exponential decay is:
### $A = P(1 - r)^t$

where:
- $A$ is the final amount,
- $P$ is the principal amount (the initial amount),
- $r$ is the rate of depreciation, and
- $t$ is the time in years.

## Step 3
We can rearrange the formula to solve for $t$:

### $t = \frac{\log(A/P)}{\log(1 - r)}$

## Step 4
Substitute the given values into the formula:

### $t = \frac{\log(7200/20700)}{\log(1 - 0.08)}$

## Step 5
Calculate the value of $t$. The result is approximately 10 years.