[tex]V\left(x\right)=14995\left(0.72\right)^x[/tex]
(a)
Graphing the function from x = 0 to x = 10:
b)
Evaluate the function for x = 5
[tex]\begin{gathered} V\left(5\right)=14995\left(0.72\right)^5 \\ V\left(5\right)\approx2901.41 \end{gathered}[/tex]
Answer:
$2901.41
c)
Let's solve the following inequality:
[tex]V\left(x\right)<1000[/tex]
so:
[tex]\begin{gathered} \left(0.72\right)^x<\frac{1000}{14995} \\ x<\frac{1}{ln\left(0.72\right)}*ln\left(\frac{1000}{14995}\right? \\ x>8.2 \end{gathered}[/tex]
Approximately after 8.2 years.
d)
[tex]4300=14995\left(y\right)^5[/tex]
Let's solve the previous equation in order to find the rate y:
[tex]\begin{gathered} y^5=\frac{4300}{14995} \\ y=\sqrt[5]{\frac{4300}{14995}} \\ y\approx0.78 \end{gathered}[/tex]
The depreciation rate is approximately:
[tex]0.78[/tex]
It depreciates 22% per year
