Category Archives: MAT 107

Argosy University MAT 107 Module 5 Assignment 1 LASA 2 Bacterial Growth NEW

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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:
1.      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.
1.      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:
1.      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.
1.      Compute the total number of bacterial cultures observed after 24 hours of growth assuming that the growth follows a geometric series.
1.      Repeat steps 1–4 for all five bacterial samples.

 

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Argosy University MAT 107 Module 3 Assignment 2 LASA 1 Compound Interest NEW

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A common component of investing money is to take advantage of a financial institution’s willingness to pay compound interest. Compound interest is basically interest paid on a deposit that continually accumulates interest. In general, the formula for compound interest can be represented by the following exponential function:

In this formula, P(t) represents the total money in the account after t years given the interest rate k which is compounded continuously. In this assignment, you will use this formula to explore the affect that compound interest can have over a period of time and at different interest rates.

Directions:

1. Select an amount of money that you would like to invest (for example $1000.00). This will be your P0 value.

2. Let your interest rate be k = 0.5%.

3. Write out the exponential function using the P0 and k values you have.

4. Determine the value of your investment after 1, 5, and 10 years.

5. Now, find the doubling time T for your investment. In other words, at what time would your initial deposit double in value?

6. Repeat steps 3 through 5 for k = 1%.

7. Repeat steps 3 through 5 for k = 1.5%.

In a Microsoft Word document, prepare a report that includes answers to the following:.

1. Report the results of the calculations you performed above.

2. What affect did changing the interest rate have on the rate at which your investment grew?

3. What affect did changing the interest rate have on the doubling time (time until your initial deposit doubled in size)?

4. Assume that this money is being invested in a savings account. Are the interest rates we selected realistic for such an account today?

5. Consider the formula we used to determine the future value of our deposit. Is this formula a realistic approximation of what we could expect from an investment or are there other issues or factors that must be considered?

6. Besides savings accounts, what other kinds of investment accounts or programs are typically offered at your bank? Do these accounts use compound interest? What are the typical interest rates for these accounts?

Use your textbook or another reference to research how to calculate simple interest. Given what you know about compound and simple interest, which would you prefer that your investment programs were based upon? Why?

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