# The resale value of a textbook decreases by 25% with each previous owner. A new textbook is sold for $85. What is the function represents the resale value of the textbook after x owners? ##### 2 Answers May 2, 2017 It is not linear. It is an exponential function. #### Explanation: If a new book worths$85, then used once book worths $63.75. Used twice book worths$47.81

Used three times book worths $35.86 etc. Now your equation (I computed this using Microsoft Excel) $V a l u e = 85 \cdot \exp \left(- 0.288 \cdot x\right)$x represents owner number. For example 5th owner of the book buys this book $V a l u e = 85 \cdot \exp \left(- 0.288 \cdot 5\right)$Value=$20.14

etc.

May 2, 2017

N_x=$85(1-25/100)^x Where ${N}_{x}$is the ${x}^{\text{th}}$new price #### Explanation: Let new cost after each sale be $N$$\textcolor{b l u e}{\text{First depreciation}}$The first reduction is:" "N_1=$85-(25/100xx$85) This is the same as:" "N_1=$85(1-25/100)

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$\textcolor{b l u e}{\text{Second depreciation}}$

Set as a=$85(1-25/100) larr" first depreciation" ${N}_{2} = a - \left(\frac{25}{100} \times a\right)$${N}_{2} = a \left(1 - \frac{25}{100}\right) \leftarrow \text{ second depreciation}$But a=$85(1-25/100) giving

N_2=$85(1-25/100)(1-25/100) larr" second depreciation" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This process repeats for each successive depreciation. So for $x$sales we have: N_x=$85(1-25/100)^x
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$\textcolor{b l u e}{\text{Example - set } x = 5}$

N_5=$85(1-25/100)^5 N_5=$85(0.75)^5 = \$20.17 to 2 decimal places