GGG Summative Review 2022
1.
Name: ___________________________________
2. A bathtub is being filled at a rate of 2.5 gallons per minute.
The bathtub will hold 20 gallons of water.
a. Complete the table showing how the water fills the bathtub.
Time
(minutes)
0
1
2
3
4
5
6
7
8
Gallons of
water
b. Graph the data from the table:
c. Write an equation for the relationship between the gallons of water in the bathtub
“y” based on the time in minutes “x”.
3. A single bacterium (measured in millimeters squared {mm 2}) lands on your teeth.
Because you didn’t brush your teeth, the bacterium starts quadrupling every hour.
a. Complete the table showing how the bacteria grows on your teeth.
Time
(hours)
0
1
2
3
4
5
6
Amount of
Bacteria
b. Graph the data from the table:
c. Write an equation for the relationship between the amount of bacteria growing on
your teeth in mm2 “y” based on the time in hours “x”.
4. Find the growth factor if the growth rate is 46%. _______________________
5. Find the growth rate if the growth factor is 1.13. _______________________
6. Find the decay factor if the decay rate is 32%. _______________________
7. Find the decay rate if the decay factor is 0.81. _______________________
4. Use mathematical vocabulary to describe at least two differences between Question
#2 (the bathtub problem) and Question #3 (the bacteria problem).
5. Use mathematical vocabulary to describe at least two similarities between Question
#2 (the bathtub problem) and Question #3 (the bacteria problem).
6. Mr. Fitz bought a new car! At year 1, the car was valued at $49,500. He learned that
the value of the car was going to decrease $500 in value every year. In year 2, the
value decreased to $49,000. In year 3, the value of the car was $48,500 and so on…
A. Complete the table to show the value of the car “v” after “x” number of years:
Years
(x)
Value of Car
(v)
1
$49,500
2
$49,000
B. Use the pattern in the table and work
backwards to determine what the y-intercept
would be for this situation?
3
4
5
y-intercept:___________________________
6
7
C. What type of relationship does the data represent?_________________________
D. Write an equation that represents the value of the car “v” after “x” number of years.
7. The fish population in Lake Peekaboo is decreasing due to pollution. The table shows
the decay of the fish population over the last 4 years.
a. What is the starting population of fish?_____________
b. What is the decay factor?_____________
c. What is the equation that models this situation?
d. If the decay continues, what will the fish population be in 6 years?
Show work to support your answer.
8. Chen, from Investigation 4.1, finds that his ballots are very small after only a few cuts.
He decides to start with a larger sheet of paper. After his first cut, the area of the ballot
was 162 in2. After the second cut, the ballot was 81 in2. With each cut the area of the
ballot was cut in half. Complete the table to show the area of each ballot after each cut.
a. What would be the y-intercept? ______________
b. What is the decay factor? ______________
c. Write an equation for this situation:
9. A tree farm has begun to harvest a section of trees planted a number of years ago.
This relationship is modeled in the table below.
a.) Suppose the relationship between the year and the trees remaining is exponential.
Find the decay factor for this relationship.
b.) Write an equation for the relationship between time and trees remaining.
c.) Use your equation to find how many trees remain after 10 years.
d.) Use your equation to find out when fewer than 5,000 trees remain.