# 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 15*x*, 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 2 |

#### 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 |

#### Example 4

Solve for x in the exponential equation: |

#### Example 5

Solve for |

#### Example 6

Find the coefficient C and base |

#### Example 7

Is this graph an exponential or log function? |

#### Exercise 1

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

#### Exercise 2

Evaluate exponential function *y* = 100^{0.75x}10^{1.5x – 3} for *x* = 2 without using a calculator

#### Exercise 3

Evaluate exponential equation *e*^{x}*y* = *e*^{2x + 4} for *x* = 5 to three decimal places.

#### Exercise 4

Solve for *x* in the exponential equation: 3^{2x + 1} = 9^{x}

#### Exercise 5

Simplify the following equation: *y* = 16/(4^{x})

#### Exercise 6

Solve for *x* in the exponential equation: 9^{-5x}9^{17x} = 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: *e*^{4x} =* e*^{9x – 4}

#### Exercise 10

Simplify the following equation: 10^{xy} = 100^{4xy – 2}