Question

The annual rate of depreciation, x, on a car that was purchased for $9,000 and is worth $4,500 after 5 years can be found using the following equation: Graph a system of equations to approximate the value of x, the rate of depreciation. Give your answer as a percent. about 4% about 13% about 1.2% cannot be determined

Answer 1

Answer:

Step-by-step explanation:

We know that exponential formula of depreciation

$A=P(1-x)^t$

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

$A=9000(1-x)^t$

we are given

when x=5 , A=4500

so, we can plug it and solve for x

$4500=9000(1-x)^5$

$\frac{9000\left(1-x\right)^5}{9000}=\frac{4500}{9000}$

$\left(1-x\right)^5=\frac{1}{2}$

$x=-\left(\frac{1}{2}\right)^{\frac{1}{5}}+1$

$x=0.12945$

so, interest rate is 13%

now, we can plug x

and we get

$A=9000(1-0.13)^t$

$A=9000(87)^t$

Graph:

Answer 2

Answer:  --------- 13% -----------