6F Exponential Functions Investigation Questions taken from Common Core Plus Book 1
1. At the start of Pay It Forward, only one person does good deeds for 3 new people. In the next stage, these three new people each do good things for three more new people, In the next stage, these new people each do good things for three more new people, and so on.
a. Make a table that shows the number of people who will receive good deeds at each of the next seven stages of the Pay It Forward process.
b.Write a NEXT-NOW statement: c. Write a rule representing this function: y =
d. How many people will do good deeds at Stage 6?e. What stage will there be 81 people doing good deeds?
2. Consider now how the number of good deeds would grow if each person touched by
thePay It Forward process were to do good deeds for only two other new people, instead of three.
a. Make a table that shows the number of people who will receive good deeds at each of the next seven stages of the Pay It Forward process.
Stage / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7# of people
doing good deeds / 1 / 2
b. Write a NEXT-NOW statement: c. Write a rule representing this function: y =
d. How many people will do good deeds at Stage 3?e. What stage will there be 64 people doing good deeds?
3. Infections seldom start with a single bacterium.
Suppose that you cut yourself on a rusty nail that puts 25 bacteria cells into the wound.
Suppose also that those bacteria each divide in two after every quarter of an hour.
# of ¼ hour periods / 0 / 1 / 2 / 3 / 4# of Bacteria in the Cut / 25 / 50
a. Complete a table showing the first several numbers in the bacteria growth .
b. Write a NEXT-NOW statement to write a rule showing how the number of bacteria changes from one quarter-hour to the next, starting from 25 at t = 0.
Next = Now Starting at
c. Write a rule showing how to calculate the number of bacteria N in the cutafter x quarter-hour time periods.
y= ______
d. Use the rules in Parts b and c to calculate the number of bacteria after 120 minutes.(hint: how many ¼ hours are in 120min.?)
e. In8 hrs? (hint: how many ¼ hours are in 8 hours?)
4. Investigate the number of bacteriaafter 2 hours if the starting numberof bacteria is 30 and divides in 2 every 15 minutes
y=NEXT = NowAfter 2 hours there are ______
5-10.The following represent the growth of bacteria in a wound.
a.What was the number present to begin the infection? b. How fast was the infection growing every ¼ hour?
5. N = 100(3)t 6. N = 48(5)t7. N = 500(2)t8. N = 50(4)t 9. N = 25(3)t 10. N = 600(2)t
a. b. a. b. a. b. a. b. a. b. a. b.
Exponential DECAY/DECLINE/DECREASE:
11. Suppose a new golf ball drops downward from a height of 27 feet onto a paved parking lot and keeps bouncing up and down, again and again. The rebound height of the ball should be of its drop height.
a. Fill in the table and plot of the data showing expected heights of the bouncesof the golf ball. Round to nearest tenth.
Bounce Number / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8Rebound Height (in ft) / 27
b. Next = Now______Starting at______.c.y = ______
d. Write the function rule if the same ball drops from only 15 feet.
e.Since the ball regained 2/3 of its height, how much height did the ball lose?
f. What would the equation be if it lost 2/3 of its height and was dropped from 27 ft?
g. Suppose a ball was dropped from 20 ft and lost 1/5 of its height. What would the new equation be?
12 a. Suppose that a 200 gallon reservoir had 10% of its water evaporated monthly, what the equation be?
b. Suppose that a 200 gallon reservoir only retained 10% of its water each month, what would the equation be?