Answer:
Decay factor is 0.9,
The value of the car after 6 years is $10,628.82.
Step-by-step explanation:
Given,
The original value of the car, P = $20,000,
Also, the annual decreasing rate, r = 10 %,
So, the value of the car after t years,
[tex]A=P(1-\frac{10}{100})^t[/tex]
[tex]=20000(1-0.1)^t[/tex]
[tex]=20000(0.9)^t-----(1)[/tex]
Now, a function [tex]f(x) =ab^x[/tex] is called exponential function,
Where, a and b are any constant,
There are two type of exponential function,
Decay : If 0 < b < 1, where b is called decay factor,
Growth : If b > 1, where b is called growth factor,
By comparing,
Decay factor of the function (1) is 0.9,
If t = 6,
Then the value of the car after 6 years would be,
[tex]A=20000(0.9)^6=\$10628.82[/tex]
