Algebra II Module 5 DBA

logarithmic function converted into an exponential function

y = b^x <--> x = logb y

natural logarithm

y = ln x "y equals the natural log of x."

Exponential Decay Function

is a function where the amount of money or of a substance decreases exponentially as time passes. The base of the exponent must be between 0 and 1.

Exponential Growth Functions

is a function where the amount of money or of a substance increases exponentially as time passes. The base of the exponent must be greater than 1.

Change of Base Formula

logb^y=log y/log b

logarithmic function

the inverse of an exponential function

Exponential equations

to solve an exponential equation, rewrite the equation with equal bases. Since the bases are the same, the exponents must be equal in order for the equation to be true.

Negative Exponents

A negative exponent represents the reciprocal of its base.

Compound interest

A=P(1+r/n)^nt

Continuous interest

A=Pe^rt

To solve a logarithmic equation

Rewrite the exponential equation as a logarithmic equation. Solve for the variable. Check your work.

Power to Power

When a power is raised to another power, multiply the exponents.

Quotient Property

When dividing two of the same variable, subtract the exponents.

Product Property

When multiplying two of the same variable, add the exponents.

Exponential function

a function where the exponent includes a variable and the base of the function is a positive real number not equal to 1