# Intermediate Algebra Homework

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Intermediate Algebra Homework

1.  Rewrite in exponential form:log4(24)=x

a) 4^x=24

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

 [removed] \$500 on deposit for 4x years, interest paid at 8% per year, compounded annually. [removed] \$500 on deposit for x years, interest paid at 2% per year, compounded quarterly. [removed] \$500 on deposit for x years, interest paid at 2% per year, compounded annually. [removed] \$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?

 [removed] Yes, the artifact is from the early part of the Roman occupation. [removed] Yes, the artifact is from the later part of the Roman occupation. [removed] No, the artifact postdates the Roman occupation. [removed] No, the artifact was present before the Roman occupation. 4

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.

 X 0 1 2 3 4 5 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?

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

• 7 years ago
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