# Unit4Vocabulary Flashcards

1
Q

Negative Exponent Property

A

a-b = 1/ab

2
Q

Doubling Time

A

The time if takes for an exponential growth equation to double in value. Typically used in population and investment studies.

3
Q

Exponent

A

The power a number is raised to.

Ex: an where n is the Exponent

4
Q

Exponential Function

A

y = abx

5
Q

Base e Log

A

Known as the Natural Log it can be written as loge but is traditionally written as ln.

6
Q

Rationalized Denominator

A

An expression that does not contain a radical in the denominator.

7
Q

Depreciation

A

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

8
Q

Quotient of Powers Property

A
9
Q

Base 10 Log

A

Usually denoted by just log but can be written as log10. It is the base used by calculators when accessing the log key.

10
Q

Common Base Property

A

If ax = ay, then x = y

11
Q

Half Life

A

The time if takes a radioactive substance to decay to half of its initial value.

12
Q

Power of a Quotient Property

A
13
Q

Exponential Growth

A

An exponential equation that increases as the input increases.

y = y0 (1 + r)x

14
Q

Logarithm

A

The inverse of an exponential function.

Given: ax = b

Then: logab = x

What power of a equals b?

15
Q

Exponential Decay

A

An exponential equation that decreases as the input increases.

y = y0 (1 - r)x

16
Q

Inequality Property of Logarithmic Functions

A

If a < b, then logna < lognb

17
Q

Inequality Property of Exponential Functions

A

If a > b, then ax > bx

18
Q

Product of Powers Property

A

am • an = am+n

19
Q

Point-Ratio Form of Exponential Equation

A

y = y1 r(x - x1)

20
Q

Power of a Product Property

A

(ab)m = ambm

21
Q

Quotient Property of Logarithms

A
22
Q

Power Property of Logarithms

A

logaxm = mlogax

23
Q

Base

A

A number raised to a power.

Ex: ax where a is the base

24
Q

Base e

A

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

25
Q

Growth Rate

A

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

26
Q

Power of a Power Property

A

(am)n = amn

27
Q

Rational Exponent

A

A fractional exponent.

Ex: x1/2

28
Q

Antilog

A

Defined as 10 to the power.

Ex: antilog(4) = 104

29
Q

A
30
Q

Change of Base Property

A

A property to change from one base to another base when calculating logarithms.

31
Q

A

A notation used to represent the root of a number.

32
Q

Compound Interest

A
33
Q

Equality Property of Logarithmic Functions

A

If a = b, then logna = lognb

34
Q

Appreciation

A

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

35
Q

Zero Power Property

A

a0 = 1

36
Q

Product Property of Logarithms

A

logaxy = logax + logay

37
Q