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- From: Mathematics, Algebra
- Posted on: Fri 31 Jan, 2014
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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?

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

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.

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 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:

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