Today in Precalculus

• Notes: Intro to Exponential Functions (no handout)

• Homework

Exponential Functions

• Functions where the exponent is the variable. y=a•bx, where

a is non-zero and represents the initial value f(0)

b is positive and represents the base

If b>1 exponential growth

If 0<b<1 exponential decay

Exponential Functions

• Example: 5730110

2

t

Q

• The initial quantity is 10, and base is ½

Exponential Functions

• Which of the following are exponential functions? If they are, list the initial value and the base

1. y = 9x

2. y = 3•7x

3. y = x2.5

4. y = 2•0.4x

Yes, initial value is 1 and base is 9

Yes, intial value is 3 and base is 7

No, exponent is not a variable

Yes, initial value is 2 and base is 0.4

Exponential Functions

• To calculate the value of the functions, be sure to follow the order of operations.

Example: y = 3•7x x = 2

y = 3•72

y = 3•49

y = 147

Graphs

y = 2x

1

2

x

y

Graphical Transformations

y = 2x+2

12

2

x

y

Graphical Transformations

y = -2x

13

2

x

y

Exponential FunctionsDetermine the formula for the exponential function whose values are given in the following table

y = 3•4x

x y

-2 3/16

-1 3/4

0 3

1 12

2 48

Exponential FunctionsDetermine the formula for the exponential function whose values are given in the following table

x y

-2 54

-1 18

0 6

1 2

2 2/3

16

3

x

y

Homework

• Page 286: 1-12all, 25-30all but just part a