Question

Most cars depreciate in value as they age. A specific model car purchased for $14 995depreciates by 28% per year. The function that models it value over time

Answer 1

`V\left(x\right)=14995\left(0.72\right)^x`

(a)

Graphing the function from x = 0 to x = 10:

b)

Evaluate the function for x = 5

`\begin{gathered} V\left(5\right)=14995\left(0.72\right)^5 \\ V\left(5\right)\approx2901.41 \end{gathered}`

Answer:

$2901.41

c)

Let's solve the following inequality:

`V\left(x\right)<1000`

so:

`\begin{gathered} \left(0.72\right)^x<(1000)/(14995) \\ x<(1)/(ln\left(0.72\right))*ln\left((1000)/(14995)\right? \\ x>8.2 \end{gathered}`

Approximately after 8.2 years.

d)

`4300=14995\left(y\right)^5`

Let's solve the previous equation in order to find the rate y:

`\begin{gathered} y^5=(4300)/(14995) \\ y=\sqrt[5]{(4300)/(14995)} \\ y\approx0.78 \end{gathered}`

The depreciation rate is approximately:

`0.78`

It depreciates 22% per year