A car was purchased for $$ \$ 16,500 $$. Each year since, the resale value has decreased by $$ 25 \% $$. Let $$ t $$ be the number of years since the purchase. Let $$ y $$ be the resale value of the car, in dollars. Write an exponential function showing the relationship between $$ y $$ and $$ t $$.

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1. The original purchase price is $$ P = 16500 $$.

2. Each year, the car retains $$ 75\% $$ of its value, so it decreases by $$ 25\% $$. This means the multiplication factor for the resale value each year is $$ 0.75 $$.

3. After $$ t $$ years, the exponential function describing the resale value is:

$$
y = 16500 \cdot (0.75)^t
$$
The resale value $$ y $$ after $$ t $$ years is given by the function: $$ y = 16500 \cdot (0.75)^t $$

A car was purchased for \( \$ 16,500 \). Each year since, the resale value has decreased by \( 25 \% \). Let \( t \) be the number of years since the purchase. Let \( y \) be the resale value of the car, in dollars. Write an exponential function showing the relationship between \( y \) and \( t \).

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