Only click on this if you want to do a lot of math Scenario & Exponential Functions
In Biology class, we’re studying the growth of bacteria on a piece of sandwich bread after students touch it with their hands, with the goal of growing the most bacteria cells. The group results are shown below.

Group A: Group A had 4 group members touch the bread. The bacteria increased by a factor of 5 each minute, so the total number of cells can be represented by f(x) = 45x

Group B: Group B had 2 people touch the bread. The bacteria increased by a factor of 4 each minute, so the number of bacteria cells is quadrupled every minute.
Minute
Number of Cells
0
2
1
8
2
32

Group C: Group C had 9 people touch the bread and noticed that the bacteria cells doubled every minute.
Scenario
Three friends are comparing how fast their social media posts have spread with the goal of having the most shares. Their results are shown below.

Amber: Amber shared her photo with 3 friends. They continue sharing the picture every day, so the number of shares can be represented by f(x) = 34x

Ben: Ben shared his photo with 2 friends. Each of those friends share with 3 more each day, so the number of shares triples every day.
Day
Number of Shares
0
2
1
6
2
18

Carter: Carter shares his post with 10 friends, who each share the post with only 2 friends each day.
Exponential Functions

Group B:

Group C:
Exponential Functions
Ben’s social media post:f(x)=2(3)^x
Carter’s social media post:f(x)=10(2)^x
Graph each function using at least 3 points for each curve

Group A:
5 minutes: 15 minutes:
Group B:
5 minutes: 15 minutes:
Group C:
5 minutes: 15 minutes:
Predictions
Predict how many shares each student will have after 3 days and after 10 days.

Amber
3 days: 10 days:
Ben
3 days: 10 days:
Carter
3 days: 10 days:
Group A
Group A decides to open their container and touch the bread 7 times with a spoon that was used that day at lunch. The new function can be represented by f(x) = 45x+7.How does this graph compare to the original?

Amber
Amber decides to send a copy of her picture to 45 residents at her grandmother’s assisted living facility. The new function can be represented by f(x) = 34x+45.How does this graph compare to the original?

Results
Results & What Would You Do?
Which group’s bacteria grew fastest? How is this shown in the equation form of the functions?

Results
Which student’s post traveled fastest? How is this shown in the equation form of the functions?

What would you do?
If you had to choose, would you prefer starting the experiment with more people touching it initially, but smaller growth, like Group C, or have fewer people touch the bread with a higher rate of growth? Justify your answer with calculations from the previous questions.

What would you do?
If you had to choose, would you prefer a post with fewer shares initially but more shares, like Amber, or a post with more friends initially but fewer shares? Justify your answer with calculations from previous questions.