122 Math 120 – 08: Quiz #6 (Chapter 4: Take-Home) Name:
Fall 2012
You may use your notes, but no other source (including internet and other people).
Show work when possible. Incorrect answers with no work will receive no credit.
Correct answers with no support may not receive full points.
For this quiz, no graphical methods will be accepted for solving equations.
1. Bismuth-214 (Bi-214) is a substance that decays by 3.46% per minute. Initially there are
50mg of Bi-214 in a container.
(a) Give a formula for the amount of Bi-214 remaining after x minutes.
(b) How much is remaining after 252 seconds?
(5 points)
(5 points)
(c) How long before only 38mg of Bi-214 remain? Give an exact answer and a 2decimal approximation. (8 points)
(d) Calculate the half-life of Bi-214. Give both an exact answer as well as a 2-decimal
approximation. (8 points)
2. Show that each of the following tables represents an exponential function, and then find a
formula for the function (do not use regression). (10 points each)
(a)
x
0
y
8.4
x
1
y
42.5
2
4
6
9.08544 9.82682 10.62868
(b)
2
5
7
36.125 22.18527 16.02885
3. Use the properties of logarithms to compute the value of each of the following given that
log A = 5, log B = -2, and logC = 4 . (6 points each)
(
(a) log A3 B 2 C
)
æ 1000A 2 B ö
(b) log ç
÷
3
è C
ø
Hint:
C =C
1
2
4. Solve each of the following equations. Give both an exact answer as well as a 3-decimal
place approximation for each. Do not use graphical techniques for these. (8 points each)
(a) log ( x - 5) - log ( x - 2) = -2
(b) 2.8ln ( 2x + 3) - 2.2 = 9.28
(c) 6.2 (1.38) - 7.4 = 44.68
x
(d) 4.6 ( 2.5844) = 40.48 (1.82)
x
x
5. The formula D = D (T ) = 406.4 ( 0.906) gives the number of days D that milk will stay fresh
T
when it is stored at a temperature of TF.
(a) How long will milk stay fresh if it is stored at 40F?
(4 points)
(b) At what temperature should milk be stored if we want it to stay fresh for 12 days?
Give an exact answers as well as a 2-decimal place approximation. (7 points)
(c) Rewrite this equation so that it gives T in terms of D.
(7 points)
6. The body weight of a mouse, W, measured in grams T weeks into an experiment is given by
W = W (T ) =11.30 + 7.37ln (T + 2) . (7 points each)
(a) When will the mouse weigh 28g?
approximation.
Give an exact answer and a 2-decimal
(b) Rewrite the equation so that it gives T in terms of W.