Unit 7: Logarithmic Functions Assignment Booklet 7 Name: < > Date: < > Unit 7: Logarithmic Functions Unit Assignment Read the course material and complete the practice questions in the Unit 7 Logarithmic Functions Guide for Learning Booklet before working on this Unit Assignment. The following chart shows you which lesson to review if you're having difficulty with the questions in this assignment booklet. Unit Assignment Questions Lesson 1, 2 7A 3, 4, 5, 6, 11 7B 7, 8, 9 7C 10 7D 12 *Logic and Reasoning *Contact your teacher if you need help with Logic and Reasoning. For full marks, show all calculations, steps, and/or explain your answers. Total Marks: 54 Type your answers within the blue brackets < >. They expand as you type. 1. Complete the following chart to analyze the characteristics of each logarithmic function. (10 marks - 0.5 each) Equation y log x y 2 log x y 2 log x y log 2 x Graph Domain <> <> <> <> Range <> <> <> <> Coordinates < > of intercept(s) <> <> <> End <> <> <> <> ADLC Mathematics 30-2 1 Assignment Booklet 7 Unit 7: Logarithmic Functions Behaviour 2. Each of the equations below was graphed on a calculator, using the following window settings: X: [-10, 10, 1] Y: [-10, 10, 1] Match each equation with its corresponding graph and write the equation on the line below the graph. (3 marks - 0.5 marks each) y 10 x y 2x y 0.5 x y log x y log 0.5 x y 3log5 x 3. 2 <> <> <> <> <> <> Write each exponential equation in logarithmic form. a. y 5x (1 mark) <> ADLC Mathematics 30-2 Unit 7: Logarithmic Functions Assignment Booklet 7 b. 4. Write each logarithmic equation in exponential form. a. y log x (1 mark) <> b. 5. x 75 y (1 mark) <> y log 2 x (1 mark) <> Place the following logarithmic expressions in order from least to greatest. (2 marks) a. b. c. d. e. log 7 65 ln10 log3 100 log10 log100 2 log 510 log5 4 <> 6. A student is asked to find the value of the following logarithmic function without using technology. Explain how the student can do this, showing all steps and the correct answer. (2 marks) y log3 729 <> 7. Match the expanded logarithmic expression in the left column with the simplified form of the expression in the right column. (6 marks) ADLC Mathematics 30-2 a. Expanded Form logb A logb B Simplified Form logb AC B i. b. logb A logb B ii. logb ABC c. C logb A logb B iii. AC logb B 3 Assignment Booklet 7 Unit 7: Logarithmic Functions d. e. f. 8. 9. logb A logb C log b A logb B logb C iv. A logb B v. logb ( AB) vi. logC A a. <> b. <> c. <> d. <> e. <> f. <> Solve the following logarithmic equations algebraically. Express your answers to the nearest hundredth, if necessary. (5 marks - 1 mark each) a. log x 5 <> b. log x 64 3 <> c. log 2 x 2 <> d. log 3 6 x <> e. log 4 4 x 5 <> Solve the following exponential equations, algebraically using logarithms. Then, check your answer using technology. Express your answers to the nearest tenth. a. 4 log b A logb B logb C 4 x 85 b. 5 x3 7 c. 2 x 5 3x 8 Algebraically (2 marks) <> Algebraically (2 marks) <> Algebraically (2 marks) <> Graphically (1 mark) Graphically (1 mark) Graphically (1 mark) y1 < > y1 < > y1 < > y2 < > y2 < > y2 < > ADLC Mathematics 30-2 Unit 7: Logarithmic Functions Assignment Booklet 7 Coordinates of intersection (< > , < > ) Coordinates of intersection (< > , < > ) Coordinates of intersection (< > , < > ) Solution x < > Solution x < > Solution x < > 10. The Spanish flu was a worldwide epidemic that began in 1918 and lasted approximately 2 years. During the first few months of the epidemic, the flu spread rapidly through a Canadian city as shown in the table below. Time (months) 0 1 2 3 4 5 Number of Confirmed Cases 150 345 828 2484 6707 14084 a. Determine the equation of the exponential regression function, in the form C abt , that models the number of confirmed cases, C, as a function of time, t. Express the values of a and b to the nearest hundredth. (2 marks) <> b. Use the exponential regression equation to determine the time that it will take, to the nearest tenth of a month, for the number of confirmed cases to equal 20 000. Show or explain how you found the answer for full marks. (2 marks) <> c. Determine the equation of the logarithmic regression function t a b ln C , that models time, t, as a function of confirmed cases, C. Express the values of a and b to the nearest hundredth. (2 marks) <> d. Use the logarithmic regression equation to determine the time it will take, to the nearest tenth of a month, for the number of confirmed cases to equal 20 000. Show your work for full marks. (2 marks) <> 11. The pH of a solution can be determined using the formula pH log H , where H is the hydrogen ion concentration in the solution. ADLC Mathematics 30-2 5 Assignment Booklet 7 Unit 7: Logarithmic Functions a. The hydrogen ion concentration of a solution is 0.008 mol/L. Calculate the pH of the solution, to the nearest tenth. (1 mark) <> b. A baking soda solution has a pH of 8.9. Algebraically determine the hydrogen ion concentration of this solution. Show all your work and express your answer in scientific notation to the nearest tenth. (2 marks) <> 12. Patterns and Games: Describing Number Patterns Three rows of a number pattern are shown below. Row 1 1 10 1 11 Row 2 12 10 2 122 Row 3 123 10 3 1233 a. Identify and describe the pattern used in the first three rows. (1 mark) <> b. Use the pattern you described above to write out Row 9. (1 mark) <> End of Assignment 6 ADLC Mathematics 30-2