Question

If the price of a car will triple every 4 years, write an equation to model the price after x four year periods and how long did it take for the price to go from $180,000 to $4,860,000?

Answer 1

`y=3^xP` where `x` is the number of four-year periods.

Explanation:

The car starts at a price of `P`.
After 4 years, (1 four-year period) it will cost `3P=3^1P`.
After 8 years (2 four-year periods) it will cost `3(3P)= 3^2P`
After 12 years (3 four-year periods) it will cost `3(3^2P)= 3^3P`
The pattern is `y=3^xP`.

You need to solve the equation

`3^x*180,000=4,860,000`
`3^x=27=3^3`
`x = 3` four-year periods
So it took 12 years.