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8TH GRADE MATH
G3 TEST REVIEW
INVESTIGATION 1 & 2
NAME:__________________________________
FORM B
1. Bobby Sue is at the dentist. She hasn’t brushed her teeth well in quite a while. The dentist estimates that 6
mm² of her teeth is covered by tooth decay. He also estimates that the area of bacteria is tripling every day.
a. If Bobby Sue does not brush her teeth soon, she will be in trouble.
Complete the table below to show how much bacteria will cover
her mouth 5 days after she leaves the dentist.
days since
first visit
first dental visit
1
2
3
4
5
b. Graph the (day, decay area) from the table above.
Be sure to label each axis.
c. Write an equation that relates the area of
bacteria to the number of days. Let x = number
of days since the first visit. Let y = area of decay.
d. Identify the y-intercept as an ordered pair.
What does the y-intercept mean in the context of this situation?
2. a. Write x5 in expanded form.
b. Write 81 as a power of 3.
decay area
(mm2)
3. Which of the following situations can be represented using exponential functions? Explain how you
determined your answer.
a. When you sign your contract (before you start your job), you get a $15,000 signing bonus. You receive
$200 for each day you work. So if you work one day, you get $15,200. If you work two days, you get a
total of $15,400. If you work three days, you get $15,600, etc.
b. If you work one day, you earn a total of $25. If you work two days, you earn a total of $50. If you work
three days, you earn a total of $75. If you work four days, you earn a total of $100. If you work five
days, you earn a total of $125, etc.
c. If you work one day, you earn a total of $450. If you work two days, you earn a total of $600. If you
work three days you earn a total of $750. If you earn a total of $900, etc.
d. If you work one day, you earn a total of $25. On your second day of work you earn $50. On your third
day you earn $100. On your fourth day you earn $200.
Choice: ________
Explanation:
Identify the growth factor and initial (starting) value in the following scenarios. Explain how you identified the
growth factor.
4.
Growth Factor
amount
Model
(2, 216)
(1,36)
(0, 6)
year
5.
x
y
0
1
6
2
12
3
24
6. 𝑦 = 5(4𝑥 )
Initial Value
7. Consider the equation 𝑦 = 5(4𝑥 )
a. Make a table.
x
0
1
2
3
4
b. Graph the equation.
y
c. What will happen to your graph if you decrease the growth factor to 2?
d. What will happen to your graph if you increase the initial factor to 10?
Study each table below. Tell whether the relationship between x and y is linear, inverse, or exponential.
Write the equation that the table represents. Explain your choice.
8.
x
y
1
96
2
48
3
32
4
24
0
1
1
3
2
9
3
27
Relationship:
6
16
Equation:
Explanation:
9.
x
y
4
81
5
243
Relationship:
Equation:
Explanation:
10.
x
y
0
2
1
9
2
16
3
23
Relationship:
Equation:
Explanation:
____
8TH GRADE MATH
G3 TEST REVIEW– INVESTIGATION 5
NAME: _________________________________
FORM A
This is a calculator free quiz.
1. Write in expanded form: 36 =
2. Write in exponential form: a•a•a•a =
Write in scientific notation.
3. 1024 =
4. 0.0053
Write in standard notation.
5. 6.43 x 10-4
6. 7 x 102
Simplify. No negative or zero exponents may be in your answer.
7. (x6)3 =
8. a• a6 • a4 =
9.
𝑥4𝑥3
𝑥6
=
𝑐5
10. 𝑐 12 =
11. x0 + 3 =
12. Approximately 3.9 x 1010 cups of ice cream are consumed in the United States per year. If the U.S. has
approximately 3 x 108 people, how much ice cream is consumed per person in a year? Show your work or
explain your thought process.
13. Fill in the following table to model a linear
relationship with a rate of change of 4.
14. Fill in the following table to model an
exponential relationship with a growth rate of 4.
x
y
x
y
0
1
2
3
4
5
1
0
1
2
3
5
1