1. 6.3 Exponential Functions

2. What We Will Learn Identify and evaluate exponential functions
Graph exponential functions
Story problems

3. Needed Vocab
Exponential function: nonlinear function in form of 𝑦=𝑎 𝑏 𝑥

4. Ex. 1 Identifying Functions
Does each table represent a linear or exponential function?
Linear – will be adding or subtracting
Exponential – y values will be multiplying or dividing
linear
Exponential +1 +1 +1 X 1 2 3 Y 4 8 16 32 x2 x2 x2 +1 +1 +1 X 1 2 3 Y 4 6 8 +2 +2 +2

5. Ex. 2 Evaluating Exponentials
𝑦=−2 5 𝑥 ;𝑥=3
Plug in 3 for x is what it is saying
Do order of operations
𝑦=−
𝑦=−2 125
𝑦=−250
𝑦= 𝑥 ; 𝑥=−2
𝑦= −2
𝑦=3 4
𝑦=12

6. Ex. 3/4/5 Graphing Graph 𝑦=4 2 𝑥 Make a table
Show work for 3 of five numbers 𝑦=
𝑦=4(2)
𝑦=8 x y -2 1 -1 2 4 8 16

7. Your Practice Graph 𝑦=4 2 𝑥−3 +2 𝑦=4 2 0−3 +2 𝑦=4 (2) −3 +2
𝑦= −3 +2
𝑦=4 (2) −3 +2 𝑦=
𝑦=.5+2
𝑦=2.5 X Y -2
2.125 -1
2.25
2.5 1 3 2 4

8. Ex. 7 Story Problems 𝑦=3 4 𝑥 Use equation to answer questions1 2 3 4 Y 12 48
192
768
𝑦=3 4 𝑥
Use equation to answer questions
What is the population in 12 hours?
𝑦= =6
In 8 days?
𝑦= =196,608
Steps
1. make table from problem
2. find out what multiplying by on bottom
If dividing, then it is multiplying by a fraction
3. write 𝑦=𝑎 𝑏 𝑥
a = 1st y-value in table
b = what multiplied by x4 x4 x4 x4