Download Unit 6 Day 4: Graphing exponential functions

Warm Up 1 – 22 - 15
2
5
7𝑥
2.
3.
9𝑦
4 0
1. (𝑥𝑦 )
1
2
5. 169
4. (5𝑦 2 )−3
radical form:
answer:
7
𝑎 ∙𝑎
2
1
3
1
2
6. 8 + 49
radical form:
answer:
7.
6
2
x y
1
2
2
𝑥
8. Write the Function Rule and find the 10th term:
2, 10, 50, 250, . . .
UNIT 6 DAY 4: GRAPHING
EXPONENTIAL FUNCTIONS
Essential Questions: What form does an exponential function
have? What does the graph of an exponential function look
like?
VOCABULARY
•
Exponential Function Form: f(x) =
•
a: starting value
•
b: multiplier
•
x: input
•
f(x): output
x
ab
Time (days)
0
1
2
3
Population
2
6
18
54
•3
•3
•3
The function that
describes this pattern
is f(x) = 2(3)x. Notice
that 2 is the starting
population and 3 is the
amount that the
population is multiplied
by each day.
Population
The table and the graph show an insect population that increase
Insect Population
55
50
45
40
35
30
25
20
15
10
5
0
0
1
2
3
4
Time (Days)
5
EXAMPLE 1
The function f(x) = 2(3)x models an insect population after x
days. What will the population be on the 5th day?
f(5) = 2(3)5
f(5) = 2(243)
f(5) = 486
The function f(x) = 1500(.995)x models a prairie dog
population after x days. How many prairie dogs will there be
in 8 years?
f(8) = 1500(.995)8
f(8) = 1500(.96…)
f(8) = ≈ 1441
EXAMPLE 2
Decide whether each table represents an exponential function.
+1
+1
+1
x
y
x
y
-1
1.5
-1
-9
0
3
1
9
3
27
5
45
1
2
6
12
•2
+2
•2
+2
•2
+2
This is an exponential
function. As the xvalues increase by a
constant amount, the
y-values are multiplied
by a constant amount.
• -1
•3
• 5/3
This is not an
exponential function.
As the x-values
increase by a constant
amount, the y-values
are not multiplied by a
constant amount.
EXAMPLE
3
Create an exponential function that models each
situation.
A piece of bread
starts out with 5
bacteria. The
bacteria multiply by
40 each hour.
f(x) = 5(40)x
x
y
0
10
1
40
2
160
3
640
f(x) = 10(4)x
EXAMPLE 4
Graph the exponential function f(x) = 3(4)x.
x
y
0
3
1
12
2
48
3
192
220
200
180
160
140
120
100
80
60
40
20
0
0
1
2
3
4
EXAMPLE 5
Graph the exponential function f(x) = -5(2)x.
x
y
0
-5
1
-10
2
-20
3
-40
0
-4 0
-8
-12
-16
-20
-24
-28
-32
-36
-40
-44
1
2
3
4
SUMMARY
Essential Questions: What form does an exponential function
have? What does the graph of an exponential function look
like?
Take 1 minute to write 2 sentences answering the essential
questions.