Exponential Functions

Notes:

Terms

Exponential Functions:
is a function that can be written in the form… *f(x) = c * ax*;
Where the number ‘c’ and ‘a’ are constants.

‘c’ is called the initial value (y-intercept). ‘a’ is called the growth factor.

If a > 1; the function is growing.

If a < 1; the function is decaying.

Growing: increasing by a FIXED percentage.

Decaying: decreasing by a FIXED percentage.

Natural Exponential Function:
is a function that can be written in the form… f(x) = ex;
Where e ≈ 2.71828…

  • ‘e’ is called Euler’s Number.

Sentences to Remember

“A positive (number) to the positive power is positive. Same can be said for a positive to the negative power.”

Formulas

Compound Interest Formula:

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.