Pre-Calculus

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1) Describe the transformations on...

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.

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:

X

Y

-10 -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

P A

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

rt A Pe

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:

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) g(x) log( x) 2

Description of transformation:

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

x-intercept in (x, y) form:

X

Y

-10 -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

P A

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

rt A Pe

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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