See the attachment for full description.1) Solve

a) e^0.05t = 1600

b) ln(4x) = 3

c) log2 (8 – 6x) = 5

d) 4 + 5e^-x = 92) 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.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) = …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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