College Algebra

# Key Equations

College AlgebraKey Equations
 definition of the exponential function definition of exponential growth compound interest formula continuous growth formula $t t$is the number of unit time periods of growth $a a$is the starting amount (in the continuous compounding formula a is replaced with P, the principal) $e e$is the mathematical constant,
 General Form for the Translation of the Parent Function $f(x)=a b x+c +d f(x)=a b x+c +d$
 Definition of the logarithmic function Forif and only if Definition of the common logarithm Forif and only if Definition of the natural logarithm Forif and only if
 General Form for the Translation of the Parent Logarithmic Function
 The Product Rule for Logarithms $log b (MN)= log b ( M )+ log b ( N ) log b (MN)= log b ( M )+ log b ( N )$ The Quotient Rule for Logarithms $log b ( M N )= log b M− log b N log b ( M N )= log b M− log b N$ The Power Rule for Logarithms $log b ( M n )=n log b M log b ( M n )=n log b M$ The Change-of-Base Formula
 One-to-one property for exponential functions For any algebraic expressionsandand any positive real numberwhereif and only if Definition of a logarithm For any algebraic expression S and positive real numbersandwhereif and only if One-to-one property for logarithmic functions For any algebraic expressions S and T and any positive real numberwhereif and only if
 Half-life formula If $k<0, k<0,$ the half-life is Carbon-14 dating $t= ln( A A 0 ) −0.000121 . t= ln( A A 0 ) −0.000121 .$ is the amount of carbon-14 when the plant or animal died is the amount of carbon-14 remaining today $t t$ is the age of the fossil in years Doubling time formula If $k>0, k>0,$ the doubling time is Newton’s Law of Cooling $T(t)=A e kt + T s , T(t)=A e kt + T s ,$ whereis the ambient temperature, andis the continuous rate of cooling.