Chapter 8 Quiz 1 Mathgeek Li

Chapter 8 Quiz 1 Mathgeek Li Chapter 8 Quiz 1 MathGeek LI Instructions This quiz covers material from Chapter 8 of the MathGeek LI course Please answer all questions to the best of your ability Show your work for full credit Total Points 100 Time Limit 60 minutes Part 1 Multiple Choice 30 points Instructions Choose the best answer for each question Circle the letter corresponding to your chosen answer Each question is worth 5 points 1 Which of the following is NOT a property of logarithms a logab logcb logca Change of Base Formula b logab logac logab c Product Rule c logab logac logab c Quotient Rule d logabn n logab Power Rule e loga1 0 Base 1 Property 2 Solve for x log2x 5 3 a x 1 b x 3 c x 5 d x 11 e x 13 3 Which of the following is the equivalent exponential form of the logarithmic equation log5125 3 a 53 125 b 35 125 c 1253 5 d 1255 3 2 e 5125 3 4 What is the domain of the function fx log3x 2 a b 2 c 2 d 2 e 2 5 Simplify the expression log749 log77 log71 a 1 b 2 c 3 d 4 e 5 6 Solve for x 3x 81 a x 2 b x 3 c x 4 d x 5 e x 6 Part 2 Short Answer 40 points Instructions Answer each question completely and show your work where applicable Each question is worth 10 points 1 Expand the following logarithmic expression using the properties of logarithms log3x 12 x 2 2 Solve the following logarithmic equation for x log2x log2x 3 2 3 Find the inverse of the function fx 5x 1 2 4 Graph the function gx log2x and identify its key features domain range asymptote intercept Part 3 Application 30 points Instructions Answer the following word problem Show your work and explain your reasoning 3 clearly Word Problem A scientist is studying the growth of bacteria in a petri dish The initial population of bacteria is 100 The scientist observes that the population doubles every 4 hours a Write an exponential function to model the population of bacteria Pt as a function of time t in hours b How many bacteria will there be after 12 hours c How long will it take for the bacteria population to reach 1600 Bonus Question 5 points Explain the difference between exponential growth and logarithmic growth and provide a realworld example for each type of growth