Unit4Vocabulary

Question 1

Negative Exponent Property

Answer 1

a^-b = 1/a^b

Question 2

Doubling Time

Answer 2

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

Question 3

Exponent

Answer 3

The power a number is raised to.

Ex: aⁿ where n is the Exponent

Question 4

Exponential Function

Answer 4

y = ab^x

Question 5

Base e Log

Answer 5

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

Question 6

Rationalized Denominator

Answer 6

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

Question 7

Depreciation

Answer 7

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

Question 8

Quotient of Powers Property

Question 9

Base 10 Log

Answer 9

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

Question 10

Common Base Property

Answer 10

If a^x = a^y, then x = y

Question 11

Half Life

Answer 11

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

Question 12

Power of a Quotient Property

Question 13

Exponential Growth

Answer 13

An exponential equation that increases as the input increases.

y = y₀ (1 + r)^x

Question 14

Logarithm

Answer 14

The inverse of an exponential function.

Given: a^x = b

Then: log_ab = x

What power of a equals b?

Question 15

Exponential Decay

Answer 15

An exponential equation that decreases as the input increases.

y = y₀ (1 - r)^x

Question 16

Inequality Property of Logarithmic Functions

Answer 16

If a < b, then log_na < log_nb

Question 17

Inequality Property of Exponential Functions

Answer 17

If a > b, then a^x > b^x

Question 18

Product of Powers Property

Answer 18

a^m • aⁿ = a^m+n

Question 19

Point-Ratio Form of Exponential Equation

Answer 19

y = y₁ r^{(x - x₁)}

Question 20

Power of a Product Property

Answer 20

(ab)^m = a^mb^m

Question 21

Quotient Property of Logarithms

Question 22

Power Property of Logarithms

Answer 22

log_ax^m = mlog_ax

Question 23

Base

Answer 23

A number raised to a power.

Ex: a^x where a is the base

Question 24

Base e

Answer 24

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) = x₀e^kt where k is growth or decay rate and t is time

Question 25

Growth Rate

Answer 25

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

Question 26

Power of a Power Property

Answer 26

(a^m)ⁿ = a^mn

Question 27

Rational Exponent

Answer 27

A fractional exponent. _Ex_: x^1/2

Question 28

Antilog

Answer 28

Defined as 10 to the power. _Ex_: antilog(4) = 10⁴

Question 29

Quotient Property of Radicals

Question 30

Change of Base Property

Answer 30

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

Question 31

Radical

Answer 31

A notation used to represent the root of a number.

Question 32

Compound Interest

Question 33

Equality Property of Logarithmic Functions

Answer 33

If a = b, then log_na = log_nb

Question 34

Appreciation

Answer 34

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

Question 35

Zero Power Property

Answer 35

a⁰ = 1

Question 36

Product Property of Logarithms

Answer 36

log_axy = log_ax + log_ay

Question 37

Product Property of Radicals