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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