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4:18 PM Sat Feb 24 (XX & ghla.myghsd.ca Mathematics | Alberia Edk gt Booklet 6 MODULE 6: Lesson 1 ASSIGNMENT Lesson 1: Exponential Functions The Module 6: Lesson 1 Assignment is worth 10 marks. The value of each question is stated in the left hand margin. 1. Complete these tasks for each of the following functions. i. Describe the transformations of the function f(x) = a(c)**" + k that occurred. ii. Sketch the graph of the function. iii. Identify the domain, range, equation of the horizontal asymptote, and intercepts. (6 marks) 4:18 PM Sat Feb 24 * 20% Aghla.myghsd.ca 5 of 16 Mathematics Assignment 30-1 Booklet & 2. The radioactive isotope molybdenum-99 is produced at Chalk River Laboratories. Molybdenum-99 has a half-life of 66 h. (2 marks) a. What is the exponential function that would describe the relationship between the percent, P of molybdenum-99 remaining after t hours? (2 marks) b. What percent of molybdenum-99 would be left after 24 h? Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 1 on Moodle. Now go to Lesson 2 on Moodle.4:18 PM Sat Feb 24 XY = & ghla.myghsd.ca Pt we-natcs Fum s grareest -1 Booklet 6 MODULE 6: Lesson 2 ASSIGNMENT Lesson 2: Exponential Equations The Module 6: Lesson 2 Assignment is worth 6 marks. The value of each question is stated in the left hand margin. (3 marks) 1. Algebraically determine the solution of the exponential equation by changing the bases. 321 _ 84x3 Verify your solution by graphing. Expectations: [J Algebraic solution is determined with an exact value. [ Full work is presented for each step [J The solution is verified graphically, not algebraically [J The graph has labeled scales, arrows, and key points (intersections, intercepts, etc.). Key points are labeled to the nearest hundredth. 4:18 PM Sat Feb 24 * 20% ghla.myghsd.ca 7 of 16 Mathematics Assignment 30-1 Booklet 6 (3 marks) 2. Trinh has decided to save money to buy a new computer. She invests $800 in an account that earns 5.0% per year, compounded quarterly. Determine how long she needs to invest her money until she has $1000. Completely explain the process you used to solve this problem graphically. Expectations: A sketch of the graph is not required O Steps for how to determine the solution are clearly described and explanation provides justification. (writing out the calculator keys is not an explanation!) O Full work is presented for each step Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 2 on Moodle. Now go to Lesson 3 on Moodle. Mathematics Assignment 30-14:18 PM Sat Feb 24 see @ ghla.myghsd.ca Pt serniatcs D1 MODULE 6: Lesson 3 ASSIGNMENT Lesson 3: Understanding Logarithms The Module 6: Lesson 3 Assignment is worth 5 marks. The value of each question is stated in the left hand margin _ _logA (3 marks) 1. The formula for the Richter magnitude, M, of an earthquake is M logA 0 Where A is the amplitude of the earthquake and A is the amplitude of a standard earthquake with a magnitude of 0. In 2011, an earthquake occurred off the Pacific coast of the Tohoku region of Japan. This earthquake, which measured 9.0 on the Richter scale, is one of the five most powerful earthquakes in the world since modern record-keeping began in 1900. By comparison, one of the largest earthquakes to hit Alberta was a magnitude 4.7 earthquake. This earthquake occurred in 1984, on the border between British Columbia and Alberta, just north of Waterton Lakes National Park. Determine how many times larger in amplitude the Tohoku earthquake was compared to the Alberta quake. Express your answer to the nearest ten thousand. 4:18 PM Sat Feb 24 * 20% ghla.myghsd.ca 9 of 16 Mathematics 30-1 Assignment Booklet & (2 marks) 2. If a third earthquake is 400 times larger in amplitude than the Alberta quake, then what is the magnitude of the third earthquake? Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 3 on Moodle. Now go to Lesson 4 on Moodle.4:18 PM Sat Feb 24 * 20% ghla.myghsd.ca 10 of 16 Mathematics Assignment 30-1 Booklet 6 MODULE 6: Lesson 4 ASSIGNMENT Lesson 4: Graphing Logarithmic Functions The Module 6: Lesson 4 Assignment is worth 6 marks. The value of each question is stated in the left hand margin. 1. Consider the functions f (x) = log2 x and g (x) = - 2 log2 (x - 3) + 4. (2 marks) a. Identify the domain and range for each function. (2 marks) b. Explain how the graph g(x) can be described as transformations of f (x).4:18 PM Sat Feb 24 see @ ghla.myghsd.ca 11 of 16 Pt vermiatcs Mo s greeesrrt -1 Booklet 6 2, The slope of a beach is influenced by the local tides, wind and wave patterns, and the size of the sand particles on the beach. In general, as the diameter in millimetres, d, of the average size of the particles on the beach increases, the slope of the beach, s, increases according to the formula s(d) = 0.159 + 0.1181 log d. (2 marks) If the slope of a particular beach is 0.005 (about a 1-m vertical climb for every 200 m in the horizontal direction), algebraically determine the average diameter (in millimetres) of a grain of sand on the beach. Round your answer to 4 decimal places. Once you have answered these questions, remember to submit your answers to your teacher according to the directions in your lesson. Finish the remainder of Lesson 4 on Moodle. Now go to Lesson 5 on Moodle