Name: Class Period: Date: Algebra 2 Honors O5C1-4 REVIEW O5C1: Graphing Exponential Functions Graph the exponential function and fill in the table to the right. You will need to draw in the x- and y- axis. 1. y = 4 ( 1 2 )x 2 4 Intercept(s) End Behavior 2. y = (3) x+1 + 4 Intercept(s) End Behavior
Fill in the table for each function. 3. y = 3 ( 1 12 )x 8 + 15 Description Write an exponential function to match each description of transformations. 4. Exponential growth base of 2 Vertical compression of 1 9 Horizontal translation left 21 Vertical translation down 31 5. The initial number of bacteria in a culture is 12,000. The culture doubles each day. a. Write an equation to model the population of bacteria after x days. Then use your calculator to graph the bacteria population over time. Equation: b. How many bacteria are there after 12 days? c. How many days will it take for the population to reach 384000 bacteria?
6. A college with a graduating class of 4000 students in the year 2008 predicts that its graduating class will grow 5% per year. a. Write an exponential function to model the number of students in the graduating class t years after 2008. Then use your calculator to graph the function. Equation: b. Estimate the graduating class in 2013. Round to the nearest whole number. O5C2: Solving Exponential Equations and Inequalities Solve each exponential equation. 7. 125 3x 4 = ( 1 25 ) 4x 2 8. ( 16 81 )3x 1 = ( 243 32 ) 4x+28 Solve each exponential inequality. 9. 9 9x+1 < ( 1 243 ) 3x+5 10. ( 27 125 )6x+6 ( 625 81 )x+12
Write an exponential function y = ab x for a graph that includes each pair of points. Check your work with your calculator. Then determine if this function represents exponential growth or decay. 11. (6,1562.5) and (9,195312.5) 12. In 2000, the world population was calculated to be 6,071,675,206. In 2008, it was 6,679,493,893. a. Write an exponential function to represent the world population after x years after 2000. Round to the nearest thousandth. b. Estimate the world population in 2017. c. Based on your equation, when would the world population have been 6 billion? 13. Suppose you decide to buy a new ipad mini 3 for $400 using your credit card. Your credit card has an annual interest rate of 16%, compounded monthly. Now suppose that you made no more purchases on your credit card, but also no payments on that purchase for 6 months. When you finally decide to pay the bill after those 6 months, how much did you pay? How much more money did delaying your payment cost you? 14. Mark and Stephanie put money in a savings account for their daughter, Juliana, when she was born. If they do not add any more to the account, after 10 years, the account will have $6476.77. If the bank paid an 8% interest rate on the money in the account compounded annually, about how much money did they originally put in the savings account?
O5C3: Graphing Logarithmic Functions Use the definition of logarithms to convert between exponential and logarithmic forms. 15. log 3 (x + 17) = 20 16. 4 (3x 7) = 1 4 Use the definition of logarithms to evaluate each logarithmic expression. 17. log 8 1 512 Fill in the table for the function. 18. y = 3log 3 (x + 17) 20 10 Description Write a logarithmic function to match each description of transformations. 19. Base 8 Vertical expansion of 4 Horizontal translation left 6 Vertical translation down 40
Graph each logarithmic function. Use the parent function and what you know about the transformations. Then fill in the table below each graph. 20. y = 2log 8 (x 1) + 6 21. y = 1 2 log1 4(x + 2) 4
O5C4: Solving Logarithmic Equations and Inequalities Solve each logarithmic equation. 22. 3x = log 6 216 23. log 9 (3x 2 ) = log 9 (2x + 1) Solve each logarithmic inequality. 24. log 5 (x 3) < 2 25. log 7 (8x + 5) > log 7 (6x 18)