math 1320083 2

MATH133 Unit 5: Exponential and Logarithmic Functions

Individual Project Assignment: Version 2A

Name (Required): __________________________________________________

Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Handwritten scanned work is not acceptable for AIU Online.

IMPORTANT: See Question 1 in Problem 2 below for special IP instructions. This is mandatory.

Problem 1: Photic Zone

1.      (State your chosen value of .)

 

 

 

2.      (Correctly round your answer to one decimal place, and show the intermediate steps in your work.)

 

 

 

3.      (Hint: ; solve this equation for . Correctly round your answer to one decimal place, and show the intermediate steps in your work.)

 

 

 

 

 

 

 

 

 

Problem 2: Compound Interest

If your last name begins with the letter	Choose an investment amount, P, between	Choose an interest rate, r, between
A–E	$5,000–$5,700	9%–9.99%
F–I	$5,800–$6,400	8%–8.99%
J–L	$6,500–$7,100	7%–7.99%
M–O	$7,200–$7,800	6%–6.99%
P–R	$7,800–$8,500	5%–5.99%
S–T	$8,600–$9,200	4%–4.99%
U–Z	$9,300–$10,000	3%–3.99%

 

Correctly round your answers to the nearest whole penny (two decimal places), and show the intermediate steps in all these calculations for full credit.

1.      Important: By Wednesday night at midnight, submit a Word document containing only your name and your chosen values from the table above for P and r. Submit this in the Unit 5 IP submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes.

 

 

2.      How much will you have in 8 years if the interest is compounded quarterly?

 

 

 

3.      How much will you have in 15 years if the interest is compounded daily?

 

 

 

4.      How much will you have in 12 years if the interest is compounded continuously? Use .

 

 

 

 

 

 

Problem 3: Newton’s Law of Cooling

1.      (Use ; correctly round your final answer to two decimal places, and show the intermediate steps in your work.)

 

 

 

2.      (State what you think  in this formula represents.)

 

 

 

3.      (Correctly round your answer to two decimal places, and show the intermediate steps in your work.)

 

 

 

 

 

 

Problem 4: Health Care Expenditures

The following health care data represent health care expenditures for years after 2000 in the United States.

Actual Year	Years After 2000 (x)	Health Care Expenditures (in billions of dollars)
2004	4	311.3
2006	6	403.1
2007	7	431.4
2008	8	465.7
2009	9	502.3

 

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1.      (Correctly round your answer to one decimal place, which is tenths of billions of dollars, and show the intermediate steps in your work.)

 

 

 

 

2.      (Correctly round your answer to one decimal place, and show the intermediate steps in your work.)

 

 

 

3.      (Insert graph here; include explanations to the other questions asked.)

 

 

 

 

4.      (State the types of transformations of the natural logarithmic function, , that will result in the following function)

 

 

 

 

 

Problem 5: Richter Scale

 

1.      (Complete the table below. Correctly round your answer to one decimal place, and show the intermediate steps in each of the calculations.)

 

 

E
0.5 x 106	0.5 x 101.2
1.0 x 108	1.0 x 103.2
1.5 x 1010	1.5 x 105.2
2.5 x 1012	2.5 x 107.2
1.6 x 1017	1.6 x 1012.2

 

2.      (Correctly round your answer to one decimal place, and show the intermediate steps in your work.) Hint: Replace M(x) by 9.2, and solve the logarithmic equation for x; then multiply x by 10^4.8 to get the value of E for this magnitude.

 

 

 

 

3.      (State which intellipath Learning Nodes helped you with this assignment.)

 

References

Exponents: Basic rules. (n.d.). Retrieved from the Purple Math Web site: http://www.purplemath.com/modules/exponent.htm

Formatting math as text. (n.d.). Retrieved from the Purple Math Web site: http://www.purplemath.com/modules/mathtext.htm