Intermediate Algebra Homework
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intermediate_algebra_homework.docx1. Rewrite in exponential form: log4(24)=x
b) x^24=4
c) 24^4=x
d) x^4=24
2. Which of the following applications does the function below model? f(x) =500(1.02)^4x
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$500 on deposit for 4x years, interest paid at 8% per year, compounded annually. |
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$500 on deposit for x years, interest paid at 2% per year, compounded quarterly. |
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$500 on deposit for x years, interest paid at 2% per year, compounded annually. |
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$500 on deposit for x years, interest paid at 8% per year, compounded quarterly. |
3. An artifact was found near Hadrian's Wall in the United Kingdom. Laboratory analysis done in 2001 showed that the artifact contained 76.2% of the C-14 found in living material. The Roman occupation of Britain started about 45 AD and lasted about 350 years. Could the artifact have been of Roman origin?
Answer
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Yes, the artifact is from the early part of the Roman occupation. |
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Yes, the artifact is from the later part of the Roman occupation. |
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No, the artifact postdates the Roman occupation. |
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No, the artifact was present before the Roman occupation. |
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4. Use your graphing calculator for this problem.
Suppose that g(x)=9x^3 and f(x) =9(3)^x. A comparison of their graphs shows:
a) g(x) >f(x) for all real numbers x
b) g(x) >f(x) for 2.4781< x < 3.0000
c) g(x) < f(x) for all real numbers x
d) g(x) >f(x) for all real numbers x> 0
5. Complete the following table of approximated y values for the given exponential function. Type in your answer as an integer.
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0 |
1 |
2 |
3 |
4 |
5 |
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F(x) |
500 |
541 |
586 |
634 |
? |
743 |
6. For a certain chemical reaction , the concentration of product C(t) as a function of time, t is given by formula C(t)-C0(1-e^-kt), where C0 is the final concentration of the product and k is the rate constant of the reaction. If k = 0.0431 per second, how many seconds will it take to reach 90% of the final concentration?
a) about 5.34 seconds
b) about 53.4 seconds
c) about 10.1 seconds
d) about 101 seconds
7. The half-life of some naturally occurring radioactive isotope is 80 years. How long would it take for a sample of this isotope to decay to one-tenth of the initial amount?
a)266
b) 80
c) 8
d) 40
