the depreciation rate r for a new car is given by the function r = 1 - (v / 46200)^(1/3), where v is the…

the depreciation rate r for a new car is given by the function r = 1 - (v / 46200)^(1/3), where v is the value of the car when it is three years old. a. what is the depreciation rate for a $46,200 luxury car that is worth $19,200 after 3 years? b. write v as a function of r.

the depreciation rate r for a new car is given by the function r = 1 - (v / 46200)^(1/3), where v is the value of the car when it is three years old. a. what is the depreciation rate for a $46,200 luxury car that is worth $19,200 after 3 years? b. write v as a function of r.

Answer

Explanation:

Step1: Substitute V value into formula

Given $r = 1-\left(\frac{V}{46200}\right)^{\frac{1}{3}}$, and $V = 19200$. First, calculate $\frac{V}{46200}=\frac{19200}{46200}=\frac{32}{77}$.

Step2: Calculate the cube - root part

$\left(\frac{32}{77}\right)^{\frac{1}{3}}=\sqrt[3]{\frac{32}{77}}\approx0.753$.

Step3: Calculate the depreciation rate r

$r = 1 - 0.753=0.247$. To convert to percentage, multiply by 100, so $r = 24.7%$.

Step4: Solve for V in terms of r

Start with $r = 1-\left(\frac{V}{46200}\right)^{\frac{1}{3}}$. Rearrange to get $\left(\frac{V}{46200}\right)^{\frac{1}{3}}=1 - r$. Cube both sides: $\frac{V}{46200}=(1 - r)^3$. Then $V = 46200(1 - r)^3$.

Answer:

a. $24.7%$ b. $V = 46200(1 - r)^3$