Exponential Growth and Decay
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In exponential growth, a quantity is multiplied by the same number over every equal time period. When a bank pays 3% interest, the amount is multiplied by 1.03 every year. After n years the account holds P · 1.03ⁿ. In decay the multiplier is less than 1 — for radioactive decay it is ½ for every half-life.
What does this generator do?
On the easy level you work out bacteria that keep doubling, decay after a whole number of half-lives and compound interest. On the medium level you calculate population growth, the falling value of a car and decay after a non-whole number of half-lives. On the hard level you look for an unknown time or yearly percentage — a logarithm or a root will help there.
How to use it
1) Find the starting value and the multiplier for one period: growth by p% is 1 + p/100, decay by p% is 1 − p/100, a half-life is ½. 2) Count how many times you multiply. 3) Calculate starting value · multiplier^number of periods. 4) Round only at the end. 5) If you are looking for the time, solve the equation with a logarithm.