Exponential and Logarithmic Equations

Notes:

Theorems/Formulas

Remember the Compound Interest Formula? (It’s alright if you didn’t, for now…)

Here it is:

A = P(1 + (r/n))nt

Where…

P => Principal

r => annual interest rate (as a decimal)

n => number of compoundings in a year

t => time in years

A => accumulated value

Now, there’s a formula for Continuously Compounded Interest.

This means roughly that interest is compunded infinitely many times per year.

Here’s the formula:

A = Pert

Where…

P => Principal

A = accumulated value

r => annual interest rate

t => time in years

e = Euler’s number

We also have the Exponential Growth and Decay Model(s):

n(t) = n(0)ert

Where…

n => whatever is growing or decaying exponentially

r => relative growth rate (as a decimal)

t => time

n(0) => initial value of ‘n’ (value of ‘n’ corresponding to when t=0)