Final Math Homework…
Assignment 1: LASA 2: Bacterial Growth
As a medical research technician, you have been assigned the task of modeling the growth of five different strains of the E. coli bacteria. These bacteria are grown in Petri dishes and exposed to the same environmental conditions (food source, pressure, temperature, light, etc.). Each hour, you count and record the number of bacterial cultures in each of the sample Petri dishes. The results for the first 7 hours of observations are recorded in the chart below:
|
Bacterial Sample |
Hour 1 |
Hour 2 |
Hour 3 |
Hour 4 |
Hour 5 |
Hour 6 |
Hour 7 |
|
1 |
16 |
64 |
256 |
1024 |
4096 |
16,384 |
65,536 |
|
2 |
97 |
291 |
873 |
2619 |
7857 |
23,571 |
70,713 |
|
3 |
112 |
784 |
5488 |
38,416 |
268,912 |
1,882,384 |
13,176,688 |
|
4 |
7 |
63 |
567 |
5103 |
45,927 |
413,343 |
3,720,087 |
|
5 |
143 |
286 |
572 |
1144 |
2288 |
4576 |
9152 |
Directions: Assuming that the growth pattern for each bacterial sample follows a geometric sequence, determine the following:
- Determine the rate at which the culture grows in a hour. This rate will be the factor r by which the number of bacterial cultures has increased since the last recorded observation.
- Write a formula that represents the growth of this bacteria based upon your observations. Your formula will be based upon the basic format for a geometric sequence:
- Using the formula you’ve developed, determine the number of cultures you would expect to see in the Petri dish on the 8th, 10th, and 12th hour of your observations.
- Compute the total number of bacterial cultures observed after 24 hours of growth assuming that the growth follows a geometric series.
- Repeat steps 1–4 for all five bacterial samples.
In a Microsoft Word document, prepare a report that includes answers to the following:
-
- Report the results of the calculations you performed above.
-
- Which strain of E. coli exhibited the highest growth rate?
-
- Which strain of E. coli exhibited the lowest growth rate?
-
- Assuming that all five of the E. coli strains present a high toxicity danger to humans, which do you suppose would be the most manageable based upon growth? Why?
-
- Consider how you’ve modeled the growth of the E. coli strains using the concept of geometric sequence. Is this a realistic approach to modeling bacterial growth?
-
- What other factors do you think should be considered when modeling the growth of bacteria such as E. coli?
- Conduct an Internet search for research on E. coli. Look for information related to growth rate, environmental conditions conducive to growth, methods of controlling growth, etc.
Assignment 2: Find the nth or general term (Show step-by-step with explanation).
5, 5a/2, 5a2/4, 5a4/8…
