MathBench > Population Dynamics

Exponential Growth and Decay

How to calculate next year’s population (or bank balance)

When you’re calculating exponential growth, it is natural to think in terms of how much you ADD each year.  In my head, I’m saying something like “OK, I started with $1050, and 5% of that is $52.50, so I have to add that to the $1050 to get (voila) $1102.50." 

This works fine if you only have to figure out one or two years worth of numbers.  But if you have to go many years into the future, it's rather a pain.  So, I’m going to show you a much faster way.

Let’s go back to the bank balance.  In addition to the money you already have, you will get another 5%.  In other words, you keep 100% of your money, and add 5% more:

100% + 5% = 105%

So really what you need to do is find 105% of your bank balance.  Remember from high school that taking a percentage is the same as moving the decimal 2 places to the left and MULTIPLYING.  So:

105% of $1050 = $1050 × 1.05 = $1102.50

 

Here are some practice questions.

What do you need to do in order to:

  1. Find tomorrow’s population of fruit flies (with a growth rate of 30%):
    multiply first year’s population by .
  2. Find next year’s balance on a $26,000 investment which is returning 9%:
    multiply $26,000 by .
  3. baby on hands and kneesFind the balance on your credit card if you don’t pay anything for a year and get charged 19% interest?:
    Multiply original amount due by .
  4. Find next year’s global human population, assuming that the growth rate is 1.2%? 
    Multiply this year’s population by .