Question

The value of a certain car after years is modeled by the expression 15,000×(0.77)ᵗ. What are the initial cost, I, and the rate of depreciation, r, of this car?

Answer 1

The initial cost of the car is $15,000 and the rate of depreciation is 23% per year.

Step-by-step explanation:

The initial cost, I, of the car is represented by the first number in the expression, which is $15,000. This is the value of the car when t is zero, meaning right at the time of purchase, before any depreciation takes place.

The rate of depreciation, r, is represented by the second number in the expression, which is 0.77. To find the rate of depreciation as a percentage, you subtract this number from 1 and then convert to a percentage. So, r = (1 - 0.77) × 100% = 23%. This means the car loses 23% of its value each year.