# MATH 133 Unit 5 Individual Project A / math133 unit 5 IP ver A - 41896

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1) Describe the transformations on the following graph of f(x) = log(x) . 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. )

Graph

a) g(x) = log(x - 5)

Description of transformation:

Equation(s) for the Vertical Asymptote(s):

x-intercept in (x, y) form:

b) g(x) = -log(x) + 2

Description of transformation:

Equation(s) for the Vertical Asymptote(s):

x-intercept in (x, y) form:

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?

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b) What was the average score after 14 months?

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c) After what time t was the average score 40%?

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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

A = P(1 + r/n)^nt

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.

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.

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c) If a bank compounds continuously, then the formula used is where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the nearest cent.

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