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MATH133 Unit 5 Individual Project – A
1) Describe the transformations on the following graph of )log()( xxf . State the
placement of the vertical asymptote and x-intercept after the transformation. For
example, vertical shift up 2 or reflected about the x-axis are descriptions.
a) g(x) = log(x – 5)
Description of transformation:
Equation(s) for the Vertical Asymptote(s):
x-intercept in (x, y) form:
b) 2)log()( xxg
Description of transformation:
Equation(s) for the Vertical Asymptote(s):
x-intercept in (x, y) form:
X
Y
-1
0
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
10
-10
–
9
–
8
–
7
–
6
–
5
–
4
–
3
–
2
–
1
1
2
3
4
5
6
7
8
9
10
0
2) Students in an English class took a final exam. They took equivalent forms of the
exam at monthly intervals thereafter. The average score S(t), in percent, after t months
was found to be given by
S(t) = 68 − 20 log (t + 1), t ≥ 0.
a) What was the average score when they initially took the test, t = 0?
Answer:
Show your work in this space:
b) What was the average score after 14 months?
Answer:
Show your work in this space:
c) After what time t was the average score 40%?
Answer:
Show your work in this space:
3) The formula for calculating the amount of money returned for an initial deposit
into a bank account or CD (certificate of deposit) is given by
nt
n
r
PA
1
A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.
Carry all calculations to six decimals on each intermediate step, then round the final
answer to the nearest cent.
Suppose you deposit $3,000 for 6 years at a rate of 7%.
a) Calculate the return (A) if the bank compounds semi-annually. Round your
answer to the nearest cent.
Answer:
Show work in this space. Use ^ to indicate the power or use the Equation
Editor in MS Word.
b) Calculate the return (A) if the bank compounds monthly. Round your answer to
the nearest cent.
Answer:
Show work in this space:
c) If a bank compounds continuously, then the formula used is
rtPeA
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the nearest cent.
Answer:
Show work in this space:
