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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?

User Nandakishore
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1 Answer

14 votes
14 votes
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{ - }(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{ - }(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

User Faesal
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