O5C1: Graphing Exponential Functions

Transcription

1 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 Intercept(s) End Behavior

2 Fill in the table for each function. 3. y = 3 ( 1 12 )x 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 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 bacteria?

3 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 Then use your calculator to graph the function. Equation: b. Estimate the graduating class in Round to the nearest whole number. O5C2: Solving Exponential Equations and Inequalities Solve each exponential equation x 4 = ( 1 25 ) 4x 2 8. ( )3x 1 = ( ) 4x+28 Solve each exponential inequality x+1 < ( ) 3x ( )6x+6 ( )x+12

4 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, ) 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 Round to the nearest thousandth. b. Estimate the world population in 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 $ 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?

5 O5C3: Graphing Logarithmic Functions Use the definition of logarithms to convert between exponential and logarithmic forms. 15. log 3 (x + 17) = (3x 7) = 1 4 Use the definition of logarithms to evaluate each logarithmic expression. 17. log Fill in the table for the function. 18. y = 3log 3 (x + 17) 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

6 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) y = 1 2 log1 4(x + 2) 4

7 O5C4: Solving Logarithmic Equations and Inequalities Solve each logarithmic equation x = log log 9 (3x 2 ) = log 9 (2x + 1) Solve each logarithmic inequality. 24. log 5 (x 3) < log 7 (8x + 5) > log 7 (6x 18)