# Logarithms and Exponential Functions

Exponential Functions

# At a Glance - Exponential Functions

Allowance day—time to go buy that new video game / pair of jeans / crazy gadget. Wait, what's that, Mom? You want me to save all of my allowance now? Lame.

Every week you put away money, watching the number tick up at the same rate: \$15, \$30, \$45. This change can be easily represented by the linear function 15x, assuming x represents weeks.

A linear function's got a constant rate of change. In other words, you add the same amount for every increase in x. Here you're adding \$15 per week to your account, or for every increase in x, you add 15.

#### Example 1

 Graph 2x and x2, determine graphically where they meet. Where in the domain of x > 0 is 2x greater than x2?

#### Example 2

 Find the function from the set {1,3 ; 2,9 ; 3,27}, is it exponential or linear?

#### Example 3

 Solve the exponential equation for y: 32x + 4 = 9y

#### Example 4

 Solve for x in the exponential equation:

#### Example 5

 Solve for x without using a calculator:

#### Example 6

 Find the coefficient C and base b for the exponential function y = Cbx from the following set: {1,4 ; 2,8 ; 5,64}

#### Example 7

 Is this graph an exponential or log function?

#### Exercise 1

Evaluate exponential function y = 3x + 2x – 4 – 2x – 2 for x = 4 without using a calculator

#### Exercise 2

Evaluate exponential function y = 1000.75x101.5x – 3 for x = 2 without using a calculator

#### Exercise 3

Evaluate exponential equation exy = e2x + 4 for x = 5 to three decimal places.

#### Exercise 4

Solve for x in the exponential equation: 32x + 1 = 9x

#### Exercise 5

Simplify the following equation: y = 16/(4x)

#### Exercise 6

Solve for x in the exponential equation: 9-5x917x = 100 to three decimal places.

#### Exercise 7

Solve the exponential equation for x to three decimal places: 1500(1.73)2x = 2500

#### Exercise 8

Solve for x in the exponential equation:

#### Exercise 9

Solve for x in the exponential equation: e4x = e9x – 4

#### Exercise 10

Simplify the following equation: 10xy = 1004xy – 2