The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. Write an exponential function for the graph.

b. Use the function in part a to find the value of the boat after 9.5 years.

For the answer to the question above,

V (n) = a * b^n, where V (n) shows the value of boat after n years.

V (0) = 3500

V (2) = 2000

n = 0

V (0) = a * b^0 = 3500

a = 3500

V (2) = a * b^2

2000 = 3500 * b^2

b = sqrt (2000/3500)

b ≈ 0.76

V (n) = 3500 * 0.76^n

We can check it for n = 1 which is close to 2500 in the graph:

V (1) = 3500 * (0.76) ^1

V (1) = 2660

And in the graph we have V (3) ≈ 1500,

V (n) = 3500 * (0.76) ^3 ≈ 1536

Now n = 9.5

V (9.5) = 3500 * (0.76) ^ (9.5)

V (9.5) ≈ 258