Respuesta :
The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.
What is the exponential function?
The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,
y = abˣ
Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.
Calculation:
Given that, a car is sold for $18,000.
So, the initial value a = 18000.
After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as
11700 = 18000(b)¹
⇒ b = 11700/18000 = 0.65
Since b < 1, the function is exponentially decaying.
Then, the value of the car after 'x' years is given by the exponential decay function as
y = 18000(0.65)ˣ
(It is given that, the rate of decrease is the same each year).
Learn more about exponential function here:
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