1) Solve: a. e^(. 05t) = 1600 Answer: 147. 56 Show your work in this space: ln?? e^0. 05t=ln? 1600 ? 0. 05t= ln? 1600 t= ln? 1600/0. 05=147. 56 b. ln(4x) =3 Answer: x= e^3/4 Show your work in this space: e^ln? 4x =e^3 4x=e^3 x= e^3/4 c. log_2?? (8-6x)? = 5 Answer: x=-4 Show your work in this space: 8-6x=2^5 -6x=32-8 -6x=24 x=-4 d. 4 + 5e^(? x) = 0 Answer: No solution. Show your work in this space: 5e^(-x)=-4 e^(-x)=-4/5 ln?? e^(-x) ? =ln? (-4/5)=undefined Since the right side is undefined, there is no solution. 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) Description of transformation: The original function (f(x) = log x) is shifted to the left 5 units horizontally. Equation(s) for the Vertical Asymptote(s): x = -5 x+5=0 x=-5 X-intercept in (x, y) form: (-4,0) Set g(x) = 0: log? (x+5)=0 x+5=? 10? ^0 x+5=1 x=-4 b) g(x)=log?? (-x)? Description of transformation: reflect about the y-axis Equation(s) for the Vertical Asymptote(s): x = 0 -x=0 x=0 X-intercept in (x, y) form: (-1,0) Set g(x) = 0: log? (-x)=0 x=? 10? ^0 x=-1 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 Answer: 68 Show your work in this space: If t = 0 then S(0)=68-20log?? (0+1)? =68-20(0)=68-0=68 What was the average score after 4 month? After 24 months? Round your answers to two decimal places Answer: S(4) = 54. 02; S(24) = 40. 04 Show your work in this space: If t = 4 then
S(4)=68-20log?? (4+1)? =68-20log? 5=68-13. 98=54. 02 If t = 24 then S(24)=68-20log? (24+1)=68-20log? 25=68-27. 96=40. 04 After what time t was the average score 50%? Round your answers to two decimal places Answer: t = 6. 94 months Show your work in this space: If S = 50 then 68-20 log? (t+1)=50 -20 log? (t+1)=-18 log? (t+1)=0. 9 t+1=? 10? ^0. 9 t=6. 94 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 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). 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 $2,000 for 5 years at a rate of 8%. a) Calculate the return (A) if the bank compounds annually (n = 1). Round your answer to the nearest cent Answer: $2938. 66 Show work in this space. Use ^ to indicate the power or use the Equation Editor in MS Word. A=2000(1+0. 08/1)^(1? 5)=2000(1. 08)^5=$ 2938. 66 b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the nearest cent