Try Again Your answer is incorrect. In 2002 , a car was purchased for \( \$ 17,000 \). Each year since, the resale value has decreased by \( 26 \% \). Let \( t \) be the number of years since 2002. Let \( y \) be the value of the car, in dollars. Write an exponential function showing the relationship between \( y \) and \( t \).

To find the exponential function that represents the relationship between the resale value of the car \( y \) and the number of years since 2002 \( t \), we can follow these steps: 1. **Identify the initial value**: The car was purchased for \( \$ 17,000 \). This is the initial value when \( t = 0 \). 2. **Determine the rate of depreciation**: The car's value decreases by \( 26\% \) each year. This means that \( 74\% \) of the car's value remains after each year. In decimal form, this is \( 0.74 \). 3. **Formulate the exponential function**: The general form of an exponential decay function is given by: \[ y = a \cdot b^t \] where: - \( a \) is the initial value, - \( b \) is the decay factor (which is \( 1 - \text{decay rate} \)), - \( t \) is the time in years. In this case: - \( a = 17000 \) - \( b = 0.74 \) 4. **Write the function**: Substituting the values into the formula, we get: \[ y = 17000 \cdot (0.74)^t \] Thus, the exponential function showing the relationship between \( y \) and \( t \) is: \[ y = 17000 \cdot (0.74)^t \]