Question

A new 2006 Honda head was values at $25000. It depresides at a rate of 13% a year.

Answer 1

Answer:

1. It's value in 2009 was $16,462.575

2. It's value in 2020 will be $3,558.

Step-by-step explanation:

The equation for the value of car after t years has the following format.

$V(t) = V(0)(1-r)^{t}$

In which V(t) is the value after t years, V(0) is the initial value and r is the ratio of depreciation.

In this problem, we have that:

$V(0) = 25000, r = 0.13$

So

$V(t) = V(0)(1-r)^{t}$

$V(t) = 25000(1-0.13)^{t}$

$V(t) = 25000(0.87)^{t}$

1. What was its value in 2009

2009 is 3 years after 2006, so this is V(3)

$V(t) = 25000(0.87)^{t}$

$V(3) = 25000(0.87)^{3}$

$V(3) = 16462.575$

It's value in 2009 was $16,462.575

2.What will be its value in 2020?

2020 is 14 years after 2006, so this is V14)

$V(t) = 25000(0.87)^{t}$

$V(14) = 25000(0.87)^{14}$

$V(14) = 3558$

It's value in 2020 will be $3,558.