Q. 103 - Precalculus Enhanced with Graphing Utilities

Question

Depreciation The price p, in dollars, of a Honda Civic DX Sedan that is x years old is modeled by

           $p\left(x\right)=16,630{(0.90)}^x$

(a) How much should a 3-year-old Civic DX Sedan cost?
(b) How much should a 9-year-old Civic DX Sedan cost? 

Step-by-Step Solution

Answer

(a)  12,123

(b)  6443

Step 1.Given information

The price p, in dollars, of a Honda Civic DX Sedan that is x years old is modeled by

$p\left(n\right)=16,630{(0.90)}^x$

Step 2.How much should a 3-year-old Civic DX Sedan cost?

Substitute 3 for x in the given function and simplify. 

$$\begin{gathered} p\left(3\right)=16,630{(0.90)}^3 \\ =16,630(0.729) \\ =12,123 \end{gathered}$$

Step 3. How much should a 9-year-old Civic DX Sedan cost?

 Replace x with 9 in the given function and simplify.

$$\begin{gathered} p\left(9\right)=16,630{(0.90)}^9 \\ =16,630(0.38742) \\ =6443 \end{gathered}$$