Algebra and Trigonometry

# Key Terms

annual percentage rate (APR)
the yearly interest rate earned by an investment account, also called nominal rate
carrying capacity
in a logistic model, the limiting value of the output
change-of-base formula
a formula for converting a logarithm with any base to a quotient of logarithms with any other base.
common logarithm
the exponent to which 10 must be raised to get$x; x;$$log 10 ( x ) log 10 ( x )$ is written simply as$log( x ). log( x ).$
compound interest
interest earned on the total balance, not just the principal
doubling time
the time it takes for a quantity to double
exponential growth
a model that grows by a rate proportional to the amount present
extraneous solution
a solution introduced while solving an equation that does not satisfy the conditions of the original equation
half-life
the length of time it takes for a substance to exponentially decay to half of its original quantity
logarithm
the exponent to which$b b$must be raised to get$x; x;$written$y= log b ( x ) y= log b ( x )$
logistic growth model
a function of the form$f(x)= c 1+a e −bx f(x)= c 1+a e −bx$where$c 1+a c 1+a$is the initial value,$c c$is the carrying capacity, or limiting value, and$b b$is a constant determined by the rate of growth
natural logarithm
the exponent to which the number$e e$must be raised to get$x; x;$$log e ( x ) log e ( x )$is written as$ln( x ). ln( x ).$
Newton’s Law of Cooling
the scientific formula for temperature as a function of time as an object’s temperature is equalized with the ambient temperature
nominal rate
the yearly interest rate earned by an investment account, also called annual percentage rate
order of magnitude
the power of ten, when a number is expressed in scientific notation, with one non-zero digit to the left of the decimal
power rule for logarithms
a rule of logarithms that states that the log of a power is equal to the product of the exponent and the log of its base
product rule for logarithms
a rule of logarithms that states that the log of a product is equal to a sum of logarithms
quotient rule for logarithms
a rule of logarithms that states that the log of a quotient is equal to a difference of logarithms