4.10.1: Key Terms

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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 $x;$ $\log_{10} (x)$ is written simply as $\log (x) .$

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 $b$ must be raised to get $x;$ written $y = \log_{b} (x)$

logistic growth model: a function of the form $f (x) = \frac{c}{1 + a e^{- b x}}$ where $\frac{c}{1 + a}$ is the initial value, $c$ is the carrying capacity, or limiting value, and $b$ is a constant determined by the rate of growth

natural logarithm: the exponent to which the number $e$ must be raised to get $x;$ $\log_{e} (x)$ is written as $\ln (x) .$

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

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