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y=a*b^x

Form of exponential functions

Parent Function

the most basic function of a family of functions, or the original function before a transformation is applied

Asymptote

An imaginary line on a graph that acts as a boundary line.

An=a(n-1)+d

Recursive (arithmetic)

An=a1+d(n-1)

Explicit (arithmetic)

Recursive (geometric)

An=a (n-1)*r

Explicit (Geometric)

An=a1*r ^(n-1)

Sn=n/2 (a1+an)

Finite Sum (arithmetic)

Sn=a1 (1-r^n/1-r)^nt

Finite Sum (geometric)

Exponential growth/decay

A=p (1+r)^n

Compounding Interest

A=p (1+r/n)^nt

A=Pe^rt

What is the application (formula) to use when the interest is compounded continuosly?

exponential decay

decreasing very quickly, but never reaching zero

exponential growth

increase starts slowly then increases very quickly to infinity

System of Non-Linear Equations

one or more non-linear equations working together

Transformations

the size and shape of the figure do not change when it is slid, flipped or turned