>>11596513Ask yourself the question: for how many things is the rate of growth tied to what's growing?
For instance,
-bacterial colonies growing on bread will increase create more bacteria per second as the colony gets larger.
-more radioactive isotopes decay the larger the sample is
-your bank account with continuously-compounded interest gains more money per day as your account balance gets larger
If you wanted to model these systems using a mathematical equation, you'd want an equation whose derivative (rate of change) is equal/proportional to itself.
f(x)=e^(rx) (along wiith f(x)=0) are the only functions that do this.
