Question

EXPONENTIAL AND LOGARITHMIC FUNCTIONSFinding a final amount in a word problem on exponential grow...A car is purchased for $23,000. After each year, the resale value decreases by 30%. What will the resale value be after 5 years?

Answer 1

Answer:

Resale Price = $3866

Explanations:

The resale value of a particular product is given by the formula:

$\begin{gathered} P=P_0\text{ + }(1\text{ - }\frac{r}{100})^t \\ \text{Where P}_0\text{ is the original amount} \\ r\text{ is the depreciation rate} \\ t\text{ is the }time\text{ in years} \\ P\text{ is the resale value} \end{gathered}$$\begin{gathered} P_0=\text{ \ 23000} \\ r\text{ = 30\%} \\ t\text{ = 5 years} \end{gathered}$

Substituting these parameters into the equation above:

$\begin{gathered} P\text{ = 23000 }(1\text{ - }\frac{30}{100})^5 \\ P=23000(1-0.3)^5 \\ P=23000(0.7^5) \\ P\text{ = 23000 ( }0.16807) \\ P\text{ = }3865.60999999 \\ P\text{ = 3866} \end{gathered}$

The resale price after 5 years is therefore, P = $3866