1.7: Exponential Growth and Decay

Main Points
Exponential growth and decay occur often in nature such as with radioactive decay and compound interest. Every growth has a time when it has doubled in value (doubling time) and a decay has a time when it is half its value (half-life). Interest can be compounded in two ways: annually and continuously, where interest is compounded a number of times in a year (known as compounding). Up to a certain point compounding can be more beneficial had doing it annually as one collects interest on an interest already paid. Annual interest is calculated using the formula: P = Po(1 + r)^t and compounding interest has: P = Poe^(rt). Most products have a present a future value.

Challenges
I do not understand why the two different compound interest formulas are the way they are. I do not understand how they were derived. Thus the same goes for present and future value.

Reflections
Its cool to think that because we know the effects of radioactivity and the half-lifes of the various materials that give it off, the time until which the area of the iodine spill could be occupied again can be calculated. This has then led to higher and better security and safety methods.