Answer:
The exponential function that describes the relationship between the resale value y (in dollars) and the number of years t since the purchase is given by:
y = 19500 * (0.78)^t
Step-by-step explanation:
Let's break down the details of the exponential function that describes the relationship between the resale value y (in dollars) and the number of years t since the purchase.
We know that the car was purchased for $19,500. Each year, the resale value decreases by 22%. This means the resale value after t years can be expressed as a fraction of the original value. Specifically, since 22% is equivalent to 0.22, the resale value after t years is 1 - 0.22 = 0.78 times the previous year's value.
This exponential decrease can be described by the function:
y = 19500 (0.78)^t
Where:
- y is the resale value of the car after t years.
- t is the number of years since the purchase.
- 19500 is the initial purchase price.
The function y = 19500 (0.78)^t represents the exponential decay in the resale value of the car after t years, based on the 22% annual decrease.
