Textbook Value

Question

The value of a certain textbook decreases according to the formula


V=45*2^0.9t
where V is the value of the textbook in dollars and t is the age of the textbook in years. What is the book worth when it is new? What is it worth when it is 2 years old? 10 years old? What is the domain and range of this function?

NOTE: Remember this is a model of a "real world" phenomenon. Don't approach such tasks with "blind mathematics". Consider the real world implications before setting down the answer(s).


Show & explain your work.

 

PLEASE WALK ME THRU SOLVING THIS ENTIRE PROBLEM. 

Answer 1

Your equation represents exponential growth not decay (decrease).
For decay, the exponent needs to be negative, or the base (the 2) would have to be between 0 and 1.

Assuming the equation should be V=45*2^-0.9t, here is what you would do:

 

At t=0 the book is new. -0.9t = 0, so

V = 45*2⁰ = 45*1 = 45.  This is the original cost.

 

At t=2, -0.9t = -1.8

V = 45*2^-1.8 = 45*0.2872 ≈ 12.92

 

At t=10,

V = 45*2^-9 = 45*0.00195 ≈ 0.09

 

Domain:

Time begins at 0 when the book is new and increases from there.

0 < t <∞

 

Range

Value begins at 45 and decreases toward zero. It can never reach zero.

0 < V ≤ 45