A pair of shoes now costs $85 and the price is expected to increase 3% each year.Approximately how many years from now will the price be $100?
Note: A 3% increase in the price means you mulitply by 103%, or by 1.03.
This is essentially a geometric series. Let t be the number of years and P the price of the shoes in dollars. Then:
So, we want to know t when P = $100.
Now take the logarithm of both sides. I personally prefer log base e = "ln", but pick which ever base you prefer. The choice does not matter.
So t = 5.5 years or so.
-Dan