Belinda is thinking about buying a car for

Part A: To determine whether the value of each car can be described by a linear or exponential function, we need to analyze the given data.
In a linear function, the value changes at a constant rate over time. If we observe the values of Car 1 and Car 2, we can see that the change in value is not constant. The decrease in value from year 1 to year 2 is not the same as the decrease from year 2 to year 3. Therefore, we can conclude that a linear function cannot be used to describe the value of each car after a fixed number of years.
In an exponential function, the value changes at an exponential rate over time. If we examine the values of Car 1 and Car 2, we can see that the decrease in value is consistent and follows a pattern. Each year, the value of both cars decreases by a certain percentage. This pattern suggests that an exponential function can be used to describe the value of each car after a fixed number of years.
Part B: Let's write the exponential functions to describe the value of each car after x years.
For Car 1, the initial value is 18,500, and it decreases by a certain percentage each year. Based on the given data, we can calculate the common ratio (r) by dividing the value of Car 1 in year 2 by its value in year 1:
$r=\frac{16,346.60}{17,390}\approx 0.9411$
Therefore, the exponential function for Car 1 can be written as:
$f(x)=18,500\times (0.9411{)}^x$
For Car 2, the initial value is 18,500, and it also decreases by a certain percentage each year. Similarly, we can calculate the common ratio (r) by dividing the value of Car 2 in year 2 by its value in year 1:
$r=\frac{16,500}{17,500}=0.9429$
Hence, the exponential function for Car 2 can be expressed as:
$f(x)=18,500\times (0.9429{)}^x$