## Unit 2 Exponential & Logarithmic Functions

In this unit we look to build on our experience with exponents and exponential functions and introduce logarithmic functions (the inverse of exponential functions).

Vocabulary

Below is a list of most of the vocabulary you should become familiar with for use in this unit and beyond.

Exponential Function Exponential Growth Exponential Decay Asymptote Growth Factor

Decay Factor Natural Base Exponential Function Continuously Compounded Interest

Logarithm Logarithmic Function Common Logarithm Logarithmic Scale

Change of Base Formula Logarithmic Equation Exponential Equation Natural Logarithm

Natural Logarithmic Function

Exponential Function Exponential Growth Exponential Decay Asymptote Growth Factor

Decay Factor Natural Base Exponential Function Continuously Compounded Interest

Logarithm Logarithmic Function Common Logarithm Logarithmic Scale

Change of Base Formula Logarithmic Equation Exponential Equation Natural Logarithm

Natural Logarithmic Function

1) Exponential Functions (Models)

An exponential function takes the general form;

If a > 0 and b > 1, the function represents exponential growth.

If a > 0 and 0 < b < 1, the function represents exponential decay.

In either case, the y intercept is (0, a), the domain is all real numbers, the asymptote is y = 0, and the range is

y > 0.

**Exponential Growth:**

*y = a*(1 +

*r*)

*x*

**Exponential Decay:**

*y = a*(1 -

*r*)

*x*

(x is an exponent, not multiplication)Remember that the original exponential formula was

(x is an exponent, not multiplication)

*y = abx*.

You will notice that in these new growth and decay functions,

the

*b*value (

*growth factor*) has been replaced either by (1 +

*r*) or by (1 -

*r*).

The growth "rate" (

*r*) is determined as

*b*= 1 +

*r*.

The decay "rate" (

*r*) is determined as

*b*= 1 -

*r*