Let's begin by translating what we know into mathematical terms.
The problem asks to write a function showing the relationship between y and t. If y is the price of the car and t is the number of years since the car was bought, which variable is independent and which variable is dependent? Does the price of the car depend on the number of years that have passed, or does the number of years that have passed depend on the price of the car?
Logically, the price of the car will depend on the number of years passed, therefore, y is a function of (depends on) t.
The original price of the car is $17,500. This is a constant and will not change, so we'll come back to this in a bit.
Every year, the value of the car (y) drops by 28%. Another way to think about it is that the value of the car is only 72% (100%-28%) of the value of the previous year. Mathematically, if x is the value of the car in year 1, in year 2, the value of the car will be 0.72x. In this problem, what is the value of the car in year 1, the year it was bought? That's right, $17,500. Let's substitute that number in. Now we have y = (17500)(0.72) to express the value of the car in year 2.
If we wanted to find the value of the car in year 3, we would take the result of 0.72(17500) and multiply it again by 0.72, to get y = (17500)(0.72)^2. This pattern shows us that the exponent is equal to the number of years that have passed... which we have already identified as the variable t. Mathematically, we now have the equation y = (17500)(0.72^t)
That's all! Be sure to check your answers to see if they make sense.
