Logarithmic help

Question

A new truck costs $35,000. The value of the truck depreciates 20% per year. Write an equation to model the depreciation and use the equation to determine how long it will take for the truck to have a value of only $5,000. Round your answer to the nearest tenth of a year. 

Answer 1

Hello, thank you for taking the time to post your question!

The general formula you want to use to model this situation is

V(t) = P(1 – r)^t

where V(t) represents the value of the truck after t years

P is the principal or initial value of the truck, meaning $35,000

r is the annual rate of depreciation, meaning 0.20

t is the time in years

plugging in those values makes the equation

V(t) = 35000(1 – 0.20)^t

V(t) = 35000(0.80)^t

To solve for the second part then you would be using V(t) = 5000 and then solving for the value of t algebraically! When I do that using logarithms I end up getting 8.72 years for the value

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Value (V) after n years is original value (35,000) times 1- depreciation (.2), to the nth power ...

V=35000*(0.8)^n

 

Now solve 5000=35000*0.8^n ... log 1/7=n*log (.8) ... can you do that?