Unit4Vocabulary Flashcards
Negative Exponent Property
a-b = 1/ab
Doubling Time
The time if takes for an exponential growth equation to double in value. Typically used in population and investment studies.
Exponent
The power a number is raised to.
Ex: an where n is the Exponent
Exponential Function
y = abx
Base e Log
Known as the Natural Log it can be written as loge but is traditionally written as ln.
Rationalized Denominator
An expression that does not contain a radical in the denominator.
Depreciation
When the value of an object decreases by a percentage over a set period of time. Can be modeled by an exponential equation.
Ex: y = 75(1 - 0.23)x
Quotient of Powers Property
Base 10 Log
Usually denoted by just log but can be written as log10. It is the base used by calculators when accessing the log key.
Common Base Property
If ax = ay, then x = y
Half Life
The time if takes a radioactive substance to decay to half of its initial value.
Power of a Quotient Property
Exponential Growth
An exponential equation that increases as the input increases.
y = y0 (1 + r)x
Logarithm
The inverse of an exponential function.
Given: ax = b
Then: logab = x
What power of a equals b?
Exponential Decay
An exponential equation that decreases as the input increases.
y = y0 (1 - r)x
Inequality Property of Logarithmic Functions
If a < b, then logna < lognb
Inequality Property of Exponential Functions
If a > b, then ax > bx
Product of Powers Property
am • an = am+n
Point-Ratio Form of Exponential Equation
y = y1 r(x - x1)
Power of a Product Property
(ab)m = ambm
Quotient Property of Logarithms
Power Property of Logarithms
logaxm = mlogax
Base
A number raised to a power.
Ex: ax where a is the base
Base e
Euler’s number represented by lowercase e. It is an irrational number with starting value 2.71828… It is used in many exponential growth and decay equations.
Ex: x(t) = x0ekt where k is growth or decay rate and t is time
Growth Rate
The percentage an exponential equation increases or decreases for each increase in the input. Can be calculated as the difference between the common ratio (base b) and 1.
If b - 1 > 0 then growth
If b - 1 < 0 then decay
Power of a Power Property
(am)n = amn
Rational Exponent
A fractional exponent.
Ex: x1/2
Antilog
Defined as 10 to the power.
Ex: antilog(4) = 104
Quotient Property of Radicals
Change of Base Property
A property to change from one base to another base when calculating logarithms.
Radical
A notation used to represent the root of a number.
Compound Interest
Equality Property of Logarithmic Functions
If a = b, then logna = lognb
Appreciation
When the value of an object increases by a percentage over a set period of time. Can be modeled by an exponential equation.
Ex: y = 100(1 + 0.14)x
Zero Power Property
a0 = 1
Product Property of Logarithms
logaxy = logax + logay
Product Property of Radicals