9514 1404 393
Answer:
$1,010
Explanation:
We can write the exponential decay function in the form ...
y = a(b^(t/T))
where 'a' is the initial value, and 'b' is the "growth" factor in time period T.
Here, the initial value is 16200, for t=0 corresponding to the year 2010.
The "growth" in value is by the factor 9300/16200 in the 2-year period between 2010 and 2012. This means we can write the exponential function as ...
y = 16200((93/162)^(t/2))
In the year 2020, the value of t is 2020 -2010 = 10, so the car value will be ...
y = 16200(93/162)^(10/2) = 16200(93/162)^5 ≈ 1010
The predicted value in 2020 is $1,010.
_____
If you like, you can "simplify" the base of the exponential factor to ...
(93/162)^(1/2) ≈ 0.75768
Then the value function becomes ...
y = 16,200(0.75768^t)