# 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 \$15, watching the number tick up at the same rate: \$15, \$30, \$45. This change can be easily represented by the linear function f (x) = 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.

We've seen these linear guys before. But what happens when we start multiplying by the same amount for every increase in x? Our new exponential buddies will have something to say about that. Read on, dear Shmooper.

#### Example 1

 If a function contains the points (1, 3), (2, 9), and (3, 27), is it most likely exponential or linear?

#### Example 2

 Solve for y: 3(2x + 4) = 9y

#### Example 3

 Solve for x: 7(7x – 3) = 49-2x

#### Example 4

 Solve for x without using a calculator:

#### Example 5

 Find an exponential function f (x) = Cbx that contains the following set of points: {(1, 4), (2, 8), (5, 64)}.

#### Exercise 1

Evaluate y = 3x + 2(x – 4) – 2(x – 2) when x = 4 without using a calculator.

#### Exercise 2

Evaluate y = 1000.75x(101.5x – 3) when x = 2 without using a calculator.

Solve for x:

ex = e(2x + 4)

Solve for x:

3(3x + 1) = 9x

Solve for x:

256 = 42x

9-5x(917x) = 81

Solve for x:

150(2)2x = 300

Solve for x:

Solve for x:

e4x = e(9x – 4)

#### Exercise 10

Solve for y:

10xy = 100(4xy – 2)