Exponential growth refers to an amount of substance increasing
exponentially. Exponential growth is a type of exponential
function where instead of having a variable in the base of the
function, it is in the exponent. Exponential decay and
exponential growth are used in carbon dating and other real-life
applications. I want to talk about exponential growth, I have an
example here the population of mice in the Duchy of Grand
Fenwick grows at a rate of 6% per year. How long will it take
for the population to double or quadruple? I have a table of
values here I wanted to show you why this is exponential growth.
Increasing at 6% per year means very year we're multiplying by
1.06 and so we get p sub 0 when t=0, p sub 0 times 1.06 when t=1
and p sub 0 times 1.06 squared when t=2 and so on. This would
suggest the formula p sub t equals p sub 0 times 1.06 to the t
and that's an exponential growth formula. Now to find the
doubling time I need to plug in twice the initial population
here. I don't know what the initial