Final answer:
To determine the value of the car after x years using an exponential function, we can use the initial value of the car and the rate of decrease. The rate of decrease can be found by dividing the decrease in value after one year by the initial value. Substituting the rate of decrease into the exponential function will give us the value of the car after x years.
Step-by-step explanation:
To determine the value of the car after x years, we can use an exponential function y. Let's assume that the rate of decrease of the car's value is r each year. The initial value of the car is $26,000, and after one year, the value decreases to $22,100. In one year, the value of the car decreases by $26,000 - $22,100 = $3900. Therefore, we can write the exponential function as:
y = 26,000 * (1 - r)^x
To find the value of r, we divide the decrease in value by the initial value after one year:
$3900 / $26,000 = 0.15 = (1 - r)
Solving for r, we find:
r = 1 - 0.15 = 0.85
Now, we can substitute r into the exponential function to find the value of the car after x years:
y = 26,000 * (1 - 0.85)^x