In AA3-1 investigation we saw that exponential functions with (h,k)=(0,0) are written in the form:
-- a is the starting value (f(0))
-- b is the rate of growth or decay (what we are multiplying by each time)
-- x is the number of times something occurs. It is often, but not always, an amount of time.
In AA3-2 we learned the 4 steps to write and solve exponential equations given a function story.
1) Identify the start value.
2) Determine the rate of growth or decay. Remember 0<b<1 is a rate of decay, and b>1 is a rate of growth.
3) Write the exponential equation.
4) Evaluate f(x) for a given value of x.
In AA3-3 we learning how to solve an exponential equation using the definition of a logarithm;
In this investigation we will put all three of these together:
