Raven’s parents bought a 20’ ski boat for $22,000. After 2 years, the boat was worth 17,500. Using x as the number of years and y as the boat value, graph the two points.

What is the projected boat value in 5 years?

Question

Raven’s parents bought a 20’ ski boat for $22,000. After 2 years, the boat was worth 17,500. Using x as the number of years and y as the boat value, graph the two points.

What is the projected boat value in 5 years?

anonymous · Answer

so assuming this is an exponential decay problem and not just a linear decay problem, the worth of the boat follows the expression P(t) = P_o*e^(kt) where P_o is your initial price, t is time in years, and k is the unknown rate of change of value.

First you need to solve for k.
You know that after 2 years P=17500. so 17500=22000*e^(k*2)

Use that to solve for k. Once you have k, you can solve for P(5)=22000*e^(k*5)