Question

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?

Answer 1

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)

`Value=85*exp(-0.288*x)`

x represents owner number. For example 5th owner of the book buys this book

`Value=85*exp(-0.288*5)`

`Value=$20.14`

etc.

Answer 2

`N_x=$85(1-25/100)^x`

Where `N_x` is the `x^("th")` new price

Explanation:

Let new cost after each sale be `N`

`color(blue)("First depreciation")`

The first reduction is:`" "N_1=$85-(25/100xx$85)`

This is the same as:`" "N_1=$85(1-25/100)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Second depreciation")`

Set as `a=$85(1-25/100) larr" first depreciation"`

`N_2=a-(25/100xxa)`

`N_2=a(1-25/100) larr" 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`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Example - set "x = 5)`

`N_5=$85(1-25/100)^5`

`N_5=$85(0.75)^5 = $20.17` to 2 decimal places