Can someone please help me answer questions #2-6? I need help by tonight. Please help as soon as possible. Thank you!

3.4.4Journal:Exponential vs. Quadratic

Journal

Algebra II Sem 2 (S4565874)

Points possible:20

Date: ____________

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:

HourNumber of bacteria03162123244485966192

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 they-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. make a table for a typical quadratic functiony=x². Go up to at leastx= 6 so it matches the raw data table. (1 point)

b. Graph the quadratic function. (1 point)

c. List all the following characteristics of quadratics. (2 points)

• What is they-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. make a table for a typical exponential functiony= 2^x. Go up to at least

x= 6 so it matches the raw data table. (1 point)

b. Graph the exponential function. (1 point)

c. List all the following characteristics of exponentials. (2 points)

• What is they-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?