Math 133 Unit 5

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NAME : MATH133 Unit 5 Individual Project – A 1) Solve: a. e.05t = 1600 Answer: Show your work in this space: b. ln(4x) =3 Answer: Show your work in this space: c. log2(8 – 6x) = 5 Answer: Show your work in this space: d. 4 + 5e‐x = 0 Answer: Show your work in this space: 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. 2) 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Y X 1 2 3 4 5 6 7 8 9 10 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 ) Description of transformation: Equation(s) for the Vertical Asymptote(s): x-intercept in (x, y) form: 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. What was the average score when they initially took the test, t = 0? Round your answer to a whole percent, if necessary. a) Answer: Show your work in this space: What was the average score after 4 months? after 24 months? Round your answers to two decimal places. b) Answer: Show your work in this space: After what time t was the average score 50%? Round your answers to two decimal places. c) Answer: Show your work in this space: 4) 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 ⎛ r⎞ A = P⎜1 + ⎟ ⎝ n⎠ 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

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