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# MAT133 Unit 5 Individual Project -A

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1) Solve
a) e^0.05t = 1600
b) ln(4x) = 3
c) log2 (8 - 6x) = 5
d) 4 + 5e^-x = 9

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

3) 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? Round your answer to a whole percent, if necessary.
b) What was the average score after 4 months? After 24 months?
c) After what time t was the average score 50%?

4) The formula for calculating the amount of money returned for an initial deposit into a bank account or CD is given by
Suppose you deposit \$2,000 for 5 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually.
b) Calculate the return (A) if the bank compounds quarterly.
c) If a bank compounds continuously, then the formula used is A =Pe^rt, where e is a constant and equals approximately 2.718282.
Calculate A with continuous compounding.

#### Solution Preview

Please see the attached file for detailed solution.

2. a) g(x) is obtained by horizontal shift f(x) left by 5 units.
The vertical asymptote of f(x) = ...

#### Solution Summary

It provides detailed explanations of various questions in MATH133 Unit 5 Individual Project -A, such as solving exponential equations, determining the transformations of the graphs, and calculating the returns from the bank deposit.

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