Problem 1: Photic Zone
(State your chosen value of k.)
(Correctly round your answer to one decimal place, and show the intermediate steps in your work.)
(Hint: I/I_0 =0.01,so 0.01= e^(-0.062x); solve this equation for x. 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.
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.
How much will you have in 8 years if the interest is compounded quarterly?
How much will you have in 15 years if the interest is compounded daily?
How much will you have in 12 years if the interest is compounded continuously? Use e≅2.718282.
Problem 3: Newton’s Law of Cooling
(Use e ≅2.718282; correctly round your final answer to two decimal places, and show the intermediate steps in your work.)
(State what you think k in this formula represents.)
(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
E(x)= -9.5904+ 229.9582 ln〖(x)〗.
(Correctly round your answer to one decimal place, which is tenths of billions of dollars, and show the intermediate steps in your work.)
(Correctly round your answer to one decimal place, and show the intermediate steps in your work.)
(Insert graph here; include explanations to the other questions asked.)
(State the types of transformations of the natural logarithmic function, f(x)=ln〖(x)〗, that will result in the following function)
E(x)= -9.5904+ 229.9582 ln〖(x)〗
Problem 5: Richter Scale
(Complete the table below. Correctly round your answer to one decimal place, and show the intermediate steps in each of the calculations.)
E x= E/E_0 M(x)≅0.6667 log〖(x)〗
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
(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 104.8 to get the value of E for this magnitude.
(State which intellipath Learning Nodes helped you with this assignment.)
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