An automobile is purchased for $23,000 is worth $2700 after seven years. Assuming that the car's value depreciated steadily from year to year.

Question

An automobile is purchased for $23,000 is worth $2700 after seven years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?

Answer 1

This is a classic growth/decay question represented by the equation: y= a*x^t

 

y= Ending Price

a= Initial Price

x= How much it decays/grows each year (greater than 1=growth, less than 1=decay)

t= time

 

Now we know the initial price, ending value, and time at year 7, so lets plug it in. 

 

2700=23,000*x⁷

 

We need to solve for how much it decays and grows each year, so we start by dividing both sides by 23,000. 

 

2700/23000= .116

 

So we rewrite the equation: 

 

.116=x⁷

 

Now we can cancel out the 7 on the x, by taking both sides to the power of (1/7)

 

.116^(1/7)= x^7*1/7     Which just equals x

 

.736=x

 

Now that that we know the depreciation amount each year, we just plug in to solve for x. 

 

y= 23000*.736³     or $9169