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

Answer:

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.

May 2, 2017

Answer:

#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