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. 7. Match the expanded logarithmic expression in the left column with the simplified form of the expression in the right column. (6 marks) 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 d. log b A logb B logb C iv. A logb B v. logb ( AB) vi. logC A e. f. ADLC Mathematics 30-2 logb A logb C log b A logb B logb C 1 Assignment Booklet 7 8. 9. 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. 2 Unit 7: Logarithmic Functions 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 < > Coordinates of intersection (< > , < > ) Coordinates of intersection (< > , < > ) Coordinates of intersection (< > , < > ) Solution x < > Solution x < > Solution x < > ADLC Mathematics 30-2 Unit 7: Logarithmic Functions Assignment Booklet 7 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. 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) <> ADLC Mathematics 30-2 3 Assignment Booklet 7 Unit 7: Logarithmic Functions 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 4 ADLC Mathematics 30-2