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Let’s say you invested 0 in a savings account at your bank at a 5% interest rate.
If your bank were to calculate the amount to pay you using simple interest, they would pay you 5% per year on your initial investment, so you would get 5% of 0, or , every year.
In science, the constant for a specific material, process, or environmental condition.
For example, most bacteria split more rapidly at room temperature than at near freezing, so the same bacteria will have a different growth rate constant even though they both decay radioactively because they are different materials.
If they use compound interest, however, they calculate your interest on the total amount in your account. The second year, you would make 5% interest on 5, or .25.
The third year, you would make 5% interest on 0.25, or .51.
All of those factors can be combined mathematically to predict the growth rate of a population of rabbits over a given time period.
For example, if you had 100 bacterial cells sitting in a petri dish and you knew that they split about once an hour, using this equation would mean that all 100 of those cells would wait 60 minutes and then all split at the same time. Instead, each bacterium splits at a different time, but after an hour has passed, you would expect them all to have split – and some of the bacteria that had split at the beginning of the hour would be starting to split again.
In other words, the population of bacteria is continuously growing over that hour, rather than doubling all at once – their growth follows the same mathematical progression as compound interest at an interest rate of 100%, assuming that the interest were being paid out continuously, as we described above.
Perhaps you've heard the expression “multiplying like rabbits,” implying a very rapid increase.
There is truth behind this expression: Starting at an age of six months, female rabbits can have a litter of up to 14 baby rabbits every month.