Chapter 5.3, Problem 103AYU

107. Depreciation The price p, in dollars, of a Honda Civic EX-L sedan that is x years old is modeled by

$p\left(x\right) = 22,265{\left(0.90\right)}^x$

(a) How much should a 3-year-old Civic EX-L sedan cost?

(b) How much should a 9-year-old Civic EX-L sedan cost?

(c) Explain the meaning of the base 0.90 in this problem.

To determine

To find:

(a) Price of 3-year-old Civic EX-L sedan cost.

Answer to Problem 103AYU

a) $16231.19$

Explanation of Solution

Given:

$p\left(x\right) = 22265{\left(0.90\right)}^x$

(a) Price of 3-year-old Civic EX-L sedan cost $=p\left(3\right) = 22265{\left(0.90\right)}^3 = 16231.19$.

To determine

To find:

(b) Price of 9-year-old Civic EX-L sedan cost.

Answer to Problem 103AYU

b) $8625.92$

Explanation of Solution

Given:

$p\left(x\right) = 22265{\left(0.90\right)}^x$

(b) Price of 9-year-old Civic EX-L sedan cost $=p\left(9\right) = 22265{\left(0.90\right)}^9 = 8625.92$.

To determine

To find:

(c) The meaning of the base $\text{0}\text{.90}$ in this problem.

Answer to Problem 103AYU

c) The base $\text{0}\text{.90}$ stands for the probabipty of depreciation price of 1-year-old Civic EX-L sedan.

Explanation of Solution

Given:

$p\left(x\right) = 22265{\left(0.90\right)}^x$

(c) The base $\text{0}\text{.90}$ stands for the probabipty of depreciation price of 1-year-old Civic EX-L sedan.