Part I. Exponentiation and Its Applications
Exponentiation Formulas
General Formula f(x)=a(b)x where a is the initial value, a≠0, b>0, and b≠0
Property f(x+1)=bf(x) where b is the growth factor
Relative Growth formula f(x)=a(1+r)x where r is the relative growth rate, a>0, r>-1
Relative Decay formula f(x)=a(1-r)x where b=1+r in f(x)=abx
Continuous Growth formula f(x)=aekx where k is the continuous growth rate
Doubling Time formula f(x)=a(2)x/t where t is the time
Half-Life formula f(x)=a(½)x/h where h is the half-life
Logistic Model formula N(t)=K/1+be-rt where b=K/N0-1; N0 is initial; r is intrinsic growth rate; t
and r measured in same unit of time
Interest Formulas
Monthly Compound Interest B(t)=B0(1+r/n)nt where B0 is initial; r is interest rate, n is number of
times interest rate applied per time period; t is time period elapsed
Continuous Compound Interest B(t)=B0ert
Installment Loans M=B0r(1+r) p/((1+r) p-1) where r is monthly interest rate; p is term of loans
in months; B0 is amount borrowed; M is monthly payment
Inverse Functions
f -1(y)=x if and only if f(x)=y
f(f -1(x))=x
(f(f -1(x)))-1 = f(x) inverse of inverse is original
Part II. Exponential and Logarithmic Function
Exponent Rules
1. a0=1
Exponentiation Formulas
General Formula f(x)=a(b)x where a is the initial value, a≠0, b>0, and b≠0
Property f(x+1)=bf(x) where b is the growth factor
Relative Growth formula f(x)=a(1+r)x where r is the relative growth rate, a>0, r>-1
Relative Decay formula f(x)=a(1-r)x where b=1+r in f(x)=abx
Continuous Growth formula f(x)=aekx where k is the continuous growth rate
Doubling Time formula f(x)=a(2)x/t where t is the time
Half-Life formula f(x)=a(½)x/h where h is the half-life
Logistic Model formula N(t)=K/1+be-rt where b=K/N0-1; N0 is initial; r is intrinsic growth rate; t
and r measured in same unit of time
Interest Formulas
Monthly Compound Interest B(t)=B0(1+r/n)nt where B0 is initial; r is interest rate, n is number of
times interest rate applied per time period; t is time period elapsed
Continuous Compound Interest B(t)=B0ert
Installment Loans M=B0r(1+r) p/((1+r) p-1) where r is monthly interest rate; p is term of loans
in months; B0 is amount borrowed; M is monthly payment
Inverse Functions
f -1(y)=x if and only if f(x)=y
f(f -1(x))=x
(f(f -1(x)))-1 = f(x) inverse of inverse is original
Part II. Exponential and Logarithmic Function
Exponent Rules
1. a0=1
