the table below shows the value in dollars of a car at the end of x years.
number of years, x 0| 1| 2| 3|
value, v(x)
(dollars) 11,000| 9,350| 7,948| 6,755
which exponential function models this situation?
We need to find an exponential function of the form v(x) = ab^x, where v(x) is the value of the car at the end of x years and a and b are constants.
First, find the common ratio between the values of consecutive years:
9,350 / 11,000 = 0.85
7,948 / 9,350 = 0.85
6,755 / 7,948 = 0.85
Since the common ratio is 0.85, our exponential function has the form v(x) = a(0.85)^x.
To find the value of a, plug in the initial value (x=0, v(x) = 11,000):
11,000 = a(0.85)^0
11,000 = a(1)
a = 11,000
So the exponential function that models this situation is v(x) = 11,000(0.85)^x.