Expert answer:Exponential vs. Quadratic–Please help with this a

  

Solved by verified expert:This is a Alg2
assignment. I have attached the pdf to complete.
This assignment came with a very short video presentation. You DO NOT
have access to the video, so I have include the transcript of the video
to help you complete. It is pretty simple and will not require more than
an hour or so of time. Thank you in advance for accurate information.
Attached is a pdf of the transcript of the video, then the actual questions that need to be answered.
transcript__exponential_vs._quadratic.pdf

344_journal_exponential.pdf

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Transcript: Exponential vs. Quadratic
This video starts with an image of a young woman in a lab coat with beakers of
brightly colored liquids next to her. The video begins when the “Play” button is
clicked.
Audio:
Hi, Teresa here. I just finished an experiment with my lab partner, Serena, and we
need your help to settle a disagreement. Here’s what happened.
[An image of a hand wearing a blue glove and holding small circular petri dish with
spots of beige colored bacteria is shown.] In our experiment, we had a culture of
bacteria in a petri dish, and we measured how fast they grew. You’d be amazed
how quickly these little guys can multiply!
Specifically, every hour we would look at the dish under a microscope. We would
count how many bacteria there were, and then enter the data into a table.
Here’s our data. [A table is shown with “Hour” in the left column and “Number
Bacteria” in the right column.
The following data are shown:
Hour: Number Bacteria
0: 3
1: 6
2: 12
3: 24
4: 48
5: 95
6: 192″]
The trouble is, when we sketched the data on a graph, we couldn’t agree on what
shape it looked like.
To me, it looked like a quadratic relationship. [“Quadratic:
” is shown.]
Serena disagrees. When she looked our sketch, she saw an exponential
relationship. [“Exponential:
” is shown.]
Would you do us a favor? Help us figure out what kind of relationship our data has!
Exponential vs. Quadratic
Scenario: Bacterial Growth
Instructions:
View the video found on page 1 of this journal activity.
Using the information provided in the video, answer the questions below.
Show your work for all calculations.
1. Conjectures (3 points: 1 point each)
a. What conjecture is being made?
b. What key details are given?
c. What is your plan of action?
2. The raw data (5 points)
Here are the data collected over 6 hours of bacterial growth:
Hour
Number of bacteria
0
3
1
6
2
12
3
24
4
48
5
96
6
192
a. Graph these data: (2 points: 1 point for layout; 1 point for the curve) Draw the axes. Label each axis with
numbers and its title. You may use different scales on each axis. Connect the points with a smooth curve.
b. Do you think your graph looks more like a quadratic or exponential function? Why do you think so? (1 point)
c. Here are some specific questions to consider when examining this graph: (2 points)
What is the y-intercept of the curve?
Is there a clear pattern of increase or decrease from point to point? If so, what is it?
What is the domain of the curve?
What is the range of the curve?
Are the values increasing or decreasing?
3. Compare with a Quadratic Function (4 points)
a. Create a table for a typical quadratic function y = x 2. Go up to at least x = 6 so it matches the raw data table.
(1 point)
x
y
-2
-1
0
1
2
3
4
5
6
b. Graph the quadratic function. (1 point)
c. List all the following characteristics of quadratics. (2 points)
What is the y-intercept of the graph?
Is there a clear pattern of increase from point to point? If so, what is it?
What is the domain of the function?
What is the range of the function?
Is the function increasing or decreasing?
Anything else?
4. Compare with an Exponential Function (4 points)
a. Create a table for a typical exponential function y = 2 x. Go up to at least
x = 6 so it matches the raw data table. (1 point)
x
y
-2
-1
0
1
2
3
4
5
6
b. Graph the exponential function. (1 point)
c. List all the following characteristics of exponentials. (2 points)
What is the y-intercept of the graph?
Is there a clear pattern of increase from point to point?
What is the domain of the function?
What is the range of the function?
Anything else?
5. Time to Make a Choice (2 points)
Do you think the bacterial growth data better match a quadratic or an exponential function? Explain why.
6. Extension: What is the life cycle of a real bacterial culture? (2 points) Take a look at a sketch of data from a
real bacterium, E. coli. This is what the number of live bacteria looks like over time.
Compare this graph with the one you plotted in question 2. How are they alike? How are they different? What do
you think is happening to the bacteria to cause the curve to look like this?

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