Rich is comparing the cost of maintaining his car with the depreciation value of the car. The value starts at $20,000 and decreases by 15% each year.
The maintanance cost is $500 the first year and increases by 28% per year.
When will the maintenance cost and the value be the same.
Please explain step by step
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The maintance cost and the value will be the same in 9 years.

Step-by-step explanation:

Exponential function:

An exponential function has the following format:

In which r is the rate of change.

The value starts at $20,000 and decreases by 15% each year.

This means that

So

The maintance cost is $500 the first year and increases by 28% per year.

This means that . So

When will the maintenance cost and the value be the same.

This is t for which:

So

The maintance cost and the value will be the same in 9 years.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: