# A new 2006 Honda head was values at $25000. It depresides at a rate of 13% a year. 1. What was its value in 2009 2.What will be its value in 2020?

###### Question:

1. What was its value in 2009

2.What will be its value in 2020?

## Answers

Answer:1. It's value in 2009 was $16,462.5752. 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.[tex]V(t) = V(0)(1-r)^{t}[/tex]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:[tex]V(0) = 25000, r = 0.13[/tex]So[tex]V(t) = V(0)(1-r)^{t}[/tex][tex]V(t) = 25000(1-0.13)^{t}[/tex][tex]V(t) = 25000(0.87)^{t}[/tex]1. What was its value in 20092009 is 3 years after 2006, so this is V(3)[tex]V(t) = 25000(0.87)^{t}[/tex][tex]V(3) = 25000(0.87)^{3}[/tex][tex]V(3) = 16462.575[/tex]It's value in 2009 was $16,462.5752.What will be its value in 2020?2020 is 14 years after 2006, so this is V14)[tex]V(t) = 25000(0.87)^{t}[/tex][tex]V(14) = 25000(0.87)^{14}[/tex][tex]V(14) = 3558[/tex]It's value in 2020 will be $3,558.