Question

The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years.

Answer 1

y = 3500(1 - 0.5)^9.5 ?

Answer 2

Hmmm... Looks to me like it takes more like TWO years to drop by 1/2. You have it dropping by 1/2 every year.

See if 9.5/2 get's you any closer.

Answer 3

Okay this may be a long shot:
\[\sqrt{\frac{2000}{3500}}=\sqrt{\frac{4}{7}}\]
Because it goes to 3500 to 2000 according to the graph.
\[3500\times \left(\frac{4}{7}\right)^{\frac{9.5}{2}}\]
Result 245.266

Answer 4

Not a long shot at all. What you have done is to determine the behavior over the first two years by approximating the value after two years. You then extended this behavior to the entire lifetime. This is fine. It just has three technical problems.

1) We don't actually know it is EXACTLY 2000. Just remember that this is one reasonable approximation and that there can be others.

2) The behavior over the first two periods may not be properly extended to future periods. You should check it out and see if it gives a reasonable result. In this case, you produced 9.5 ==> 245.266. To me, this value looks pretty reasonable.

3) 245.266 is an utterly silly number for reasons of precision. Your chart data are to the near 1000!!. Lose the decimal places. You MIGHT be able to estimate the near 10, but that might be a stretch. The near 100 is all you REALLY can expect.

Excellent work!!! Seriously, close to genius. Definitely not a long shot.