Question

The exponential decay graph shows the expected depreciation for a new boat, sell g for $3500, over 10 years.

Answer 1

Okay, the exponential function is
$g = a^{x}$
The start price of it in t=0 is 3,500, as we can see on the graph. Then, the function becomes
$g = 3500^{x}$
Let's see at t=2, where the price is g=2000:
$2000 = 3500^{x}$
Take natural logarithm:
$ln 2000 = ln 3500^{x}$
$x*ln 3500 = ln 2000$
$x = \frac{ln 2000}{ln 3500} = 0.93$
So, the difference between t=0 and t=2 is
$x_{t=0} - x_{t=2} = 1 - 0.93 = 0.07$
And then we get the change of x in one year equal to 0.035.
So, the final equation is
$g = 3500^{1-0.035t}$
You can insert any t and see that it is correct, for example t=7