Answer:
Step-by-step explanation:
We know that exponential formula of depreciation
[tex]A=P(1-x)^t[/tex]
where
P is the initial amount
x is the interest rate
A is the amount after t years
we are given
The annual rate of depreciation, x, on a car that was purchased for $9,000
so, P=9000
we can plug value it
[tex]A=9000(1-x)^t[/tex]
we are given
when x=5 , A=4500
so, we can plug it and solve for x
[tex]4500=9000(1-x)^5[/tex]
[tex]\frac{9000\left(1-x\right)^5}{9000}=\frac{4500}{9000}[/tex]
[tex]\left(1-x\right)^5=\frac{1}{2}[/tex]
[tex]x=-\left(\frac{1}{2}\right)^{\frac{1}{5}}+1[/tex]
[tex]x=0.12945[/tex]
so, interest rate is 13%
now, we can plug x
and we get
[tex]A=9000(1-0.13)^t[/tex]
[tex]A=9000(87)^t[/tex]
Graph:
