
Growth and Decay Notes
Presentation
•
Mathematics
•
9th Grade
•
Hard
Joseph Anderson
FREE Resource
9 Slides • 31 Questions
1
Exponential Functions: Growth and Decay
2
Growth Function
The constant multiplier is bigger than 1. Meaning the starting value is keeping 100% of its value and adding some percent.
3
Growth Function
we have to add the percent as a decimal to 1
1+%=b
4
Multiple Choice
When will a multiplier be a growth factor?
When the number is greater than 1
When the number is greater than or equal to 1
When the number is less than 1
When the number is less than or equal to 1
When the number is equal to 1
5
Multiple Choice
What is the growth rate for the equation?
y = 200(1.8x)
200
1.8
80%
6
Multiple Choice
Is y = 5(1.04)x growth or decay?
Growth
Decay
7
Multiple Choice
A=10(1.01)3
Growth
Decay
8
Multiple Select
Which of these functions is a growth function? Check all that apply.
f(x)=7(1.2)x
f(x)=5(0.8)x
f(x)=0.5(3)x
f(x)=3(34)x
9
Decay Function
The constant multiplier is between 0 and 1. This number comes from subtracting the decay rate from 100% of the original starting value.
10
Decay Function
we have to subtract the % as a decimal from 1:
1-%=b
11
Multiple Choice
When will a multiplier be a decay factor?
When the number is greater than 1
When the number is greater than or equal to 1
When the number is less than 1
When the number is less than or equal to 1
When the number is equal to 1
12
Multiple Choice
What is the decay rate in the following model?
A=1200(.85)6
1200
.15
.85
6
13
Multiple Choice
Growth
Decay
14
Multiple Choice
A=1200(.85)6
Growth
Decay
15
Starting Amount
The a is the starting amount & the y-intercept. (0, a)
16
Multiple Choice
SLOPE
RATE OF CHANGE
Y-INTERCEPT
COMMON RATIO
17
Multiple Choice
300
1.16
.16
x
18
Multiple Choice
What is the initial value for the equation?
y = 200(1.8x)
200
1.8
80%
19
Multiple Choice
This function represents the number of ants in a colony f(x)=3 ( 2)x
How many ants did you begin with?
There was 2 ants
There was 3 ants
The equation doesn't tell us
20
Fill in the Blanks
Type answer...
21
Fill in the Blanks
Type answer...
22
Fill in the Blanks
Type answer...
23
Fill in the Blanks
Type answer...
24
Fill in the Blanks
Type answer...
25
Fill in the Blanks
Type answer...
26
27
Multiple Choice
Which graphs represent exponential decay?
28
Multiple Choice
Which graphs represent exponential growth?
29
30
31
Multiple Choice
y = 15(35)x
y = 15(1.35)x
y = 15(0.35)x
y = 35(1.15)x
32
Multiple Choice
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
y=6(0.14)x
y=6(1+14)x
y=6(1.14)x
y=6(0.86)x
33
Multiple Choice
A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population.
Which function can be used to determine the number of deer, y, in this population at the end of t years?
y=1500(1−0.015)t
y=1500(0.015)t
y=1500(1+0.015)t
y=1500(1.5)t
34
Multiple Choice
There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month.
At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?
f(x)=417(1−0.0375)x
f(x)=417(1−3.75)x
f(x)=417(1+0.0375)x
f(x)=417(1+3.75)x
35
Multiple Choice
A population of fish starts at 8,000 and decreases by 6% per year.
What is the fish population in 10 years?
14,327
4,309
839
7,680
36
Multiple Choice
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
$176,783.29
$424,527.63
$57,357.75
$532,041,076.80
37
Multiple Choice
Moody's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
$23,219.72
$136.72
$51,710.94
$16,710.94
38
Multiple Choice
$8,881.47
$7,432.93
$8,400
$6,500
39
Multiple Choice
9766
9006
9765
5433
40
Multiple Choice
An experiment begins with 20 grams of a radioactive isotope. This isotope has a half-life. If y is the mass in grams remaining after x half-lives have elapsed, which equation represents the amount of grams the isotope will weigh after 4 half-lives?
y=20(2)4
y=4(20)21
y=20(21)4
y=20(4)21
Exponential Functions: Growth and Decay
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