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Annual interest rate r compounded n times annually:
Rate per period is r/n so multiplier (growth rate per period) is r/n.
To add interest to principal for a period multiply by growth factor (1 + r/n).
To add interest to initial principal P_0 for 1 year multiply by (1+r/n), n times.
Multiplier factor for 1 year is therefore (1 + r/n)^n.
In t years there will be n * t periods, each with growth factor (1 + r/n).
So multiplier for t years is (1 + r/n)^(nt).
The exponential function is P(t) = P_0 ( 1 + r/n)^(nt).

If we know the initial value doubling time, we can use our constructed graph of the exponential shape to model the growth of our exponential function. The graph is constructed in such a way that the y value doubles from one vertical line to the next, so the doubling time is the distance between vertical construction lines.

Logarithmic functions are inverse to exponential functions. We sketch rough graphs of y = 2^x, y = 3^x and y = e^x (e being close to 2.7, we estimate the position of this graph between the other two). We then use point on the 2^x graph to plot points on the graph of its inverse function, which we call the log_2(x) function, and do the same for our 3^x function, obtaining the graph of the log_e(x) function (which is also called the "natural log" function, denoted y = ln(x)).

We can use logarithmic functions to solve exponential equations. We do one example, then we list the rules for logarithms.