Question

If the rate of inflation is 2%, the cost of an item in future years can be found by iterating the function `c(x)=1.02x`, how do you find the cost of a $70 portable stereo in four years if the rate of inflation remains constant?

Answer 1

`75.77`

Explanation:

Note that adding on `2%` can be shown as:

`100%+2% =102% = 102/100 = 1.02`

Multiplying a quantity by `1.02` is a way of increasing it by `2%` in one step.

If this increase happens to an amount `(x)` every year we have:
`year 1 " "rarr" "year 2" "rarr" "year 3" "rarr" "year 4`
`""x" "xx1.02 rarr" "xx1.02" "xx1.02" "xx 1.02`

Therefore after `4` years, the value can be calculated as:

`70 xx 1.02^4`

`= $75.77`