need help in math review and its 21 question
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review2.pdf
Math 121 Exam 2 Review Summer 2014
1. Simplify the following completely, and write your answers using positive exponents:
a. 2 3
2 4
( 2 )
2
xy
x y
b.
3 2 2
3 4
u w
w u
c. 3 2
2 2
6
2
x
x y
2. Fill in the table below:
Exponential
Function
Initial Value Growth or Decay Growth or Decay
Factor
Growth or Decay
Rate as %
( ) ( )
( ) ( )
( ) ( ) ⁄
( ) ( ) ⁄
10 Growth 1.075
10 Decay
3. For each of the following, find the exponential function which goes through the given points:
a. ( ) ( ) b. ( ) ( )
c. ( ) ( ) d. ( ) ( )
4. Each table below has values representing either linear or exponential functions. Find the equation for each function.
x ( )f x
-2 240
-1 220
0 200
1 180
2 160
x ( )g x
0 200
10 230
20 264.5
30 304.17
40 349.8
t ( )h t
0 20000
5 18000
10 16200
15 14580
20 13122
5. Expand the following using the rules for logarithms:
a. 2 3
log( 1)x y z b. 3
log A
BC
6. Write the following as a single logarithm:
7. a. 3log 2 log( 3)K K b. 1
4 ln ln 3ln 2
T T S
8. Solve for t : Leave your answer in exact form
a. ( ) b. ( ) c. ( )
d. e. f. ( )
9. Convert the following:
a. 0.06
200 t
y e to the form
b. 2
1000(0.85) t
y to the form .
10. A cancer patient’s white blood cell count grew exponentially after she had completed chemotherapy
treatments. The equation 63(1.17)dC d describes C d her white blood cell count per milliliter d days after the treatment was completed.
a. What is the initial white blood cell count?
b. What is the daily growth factor? What is the daily growth rate?
c. Create a table of values that shows the white blood cell count from day 0 to day 10 after the chemotherapy. Round answers to the nearest integer.
d. Use logarithms to find you could solve for the doubling time.
11. If you had 100 grams of Plutonium-238, well you’d be arrested. But suppose you did. In one year, this amount would decay to 99.2 grams.
a. Find an exponential function ( )P t that gives the amount of Plutonium-238 left after t years.
b. State the decay rate.
c. How much Plutonium-238 would be left in 500 years?
d. Use logarithms to find the half-life of Plotonium-238.
12. The barometric pressure p decays continuously with respect to the height, h , and the decay rate is .128 millimeters of mercury per kilometer of height. The pressure at sea level is 750 millimeters of
mercury.
a. Find an exponential function that gives the pressure ( )p h at height h .
b. What is the half-life?
c. What is the pressure at height of 8 kilometers?
d. At what height will the pressure be 200 millimeters of mercury?
13. Assume $1,000 is invested at a nominal rate of 4.5%. Write equations that give the value of the money
t years after investing, and determine the effective interest rate for each interest compounded:
a. annually b. semiannually c. quarterly d. monthly e. continuously
14. The body eliminates drugs by metabolism and excretion. To predict how frequently a patient should receive a drug dosage, the physician must determine how long the drug will remain in the body. This is
usually done by measuring the half-life of the drug.
a. Most drugs are considered eliminated from the body after five half-lives, because the amount remaining is probably too low to cause any beneficial or harmful effects. After five half-lives, what
fraction of the original dose is left in the body? What percentage of the original dose is left in the
body?
b. The accompanying graph shows a drug’s
concentration ( )C t , in milligrams in the body over
time, t , in hours.
i. What is the initial concentration of the drug.
ii. Estimate the half-life of the drug.
iii.Construct an equation that approximates the curve.
Specify the units of your variables.
iv. How long would it take five half-lives to occur?
Approximately how many milligrams of the original
dose would be left then?
15. How long will it take $15,000 to grow to $100,000 if it is invested at 8.5% annual interest, compounded continuously?
16. Find the initial investment need so that after 10 years of 5% interest compounded monthly you would have $50,000.
17. Contaminated water contains a concentration of 4500 ppm of nasty-yucky stuff ( ppm is parts per million). Each time the water is filtered, 20% of the nasty-yucky stuff is removed.
a. Find an exponential model ( ) for the amount of nasty-yucky stuff remaining in the water after it is filtered n times.
b. What is the concentration that remains after the water is filtered 5 times.
c. How many times does the water need to be filtered so that the concentration is below 1ppm?
18. The energy magnitude, M , radiated by an earthquake measures the potential damage to man-made structures. It can be described as
2 log 2.9
3 M E
where the seismic energy, E , is expressed in joules. Show that for every increase in M of one unit, the
associated seismic energy E is increased by a factor of 32.
19. Given ( ) ( ) ( )
compute the following compositions:
a. ( ( ))
b. ( ( ))
c. ( ( ))
d. ( ( ))
20. Find the inverse of the following functions:
a. ( )
b. ( )
.
c. ( )
d. ( ) ( )
21. A house cleaner decides to charge his customers using an exponential scale to encourage them to maintain their homes more neatly between cleanings. For a cleaning that takes x hours, he charges
( ) ( ) dollars.
a. How much would it cost if it takes 1 hours to clean? 3 hours?
b. Find a formula for the inverse function ( ). What quantity does the input into ( ) represent? What does this function represent?
c. A customer receives a bill for $388.96 to clean his house. How long did it take to clean?
