Unit 5 Exponential & Logarithmic FunctionsS1-MHF4UName:______________________________U5A-(Lesson 1-6) Due date: December 13, 2022 @ 6:30 pmUltimate Due Date: December 15, 2022 @ 6:30 pmUNIT...

I have attached the document


Unit 5 Exponential & Logarithmic Functions S1-MHF4U Name:______________________________ U5A-(Lesson 1-6) Due date: December 13, 2022 @ 6:30 pm Ultimate Due Date: December 15, 2022 @ 6:30 pm UNIT 5 – ASSIGNMENT Exponential & Logarithmic Functions TOTAL MARK: 38 Instructions: Show all work for full marks. Add space if you need to. Submit ONE FILE (PDF) under Unit 5 Assignment Folder in BrightSpace. A) Knowledge/Understanding 1. Complete each of the sentences. No need to show work. [ 5 ] a) The inverse of is ___________________? = ??? ? b) Rewrite in exponential form: ___________________log 5 ? = 3? c) Rewrite in logarithmic form: ___________________?12 = 3? + 1 d) Write as a single logarithm: ___________________ log 13 log 5 e) Write as a single logarithm: (Show your work) _____________????4 + 12 ???? 4 1 2. Solve the following equations. Leave answers in exact form. [ 3, 3 ] a) 1252? = 5 ?−3 625 b) 1 − log (2? + 3) = log ? + 1( ) B) Application 4. One yeast colony of 200 cells is growing exponentially by 10% each hour. Another yeast colony of 1000 cells is diseased and its population is decreasing by 20% each hour. At what time (if any) will the two colonies have the same population? Only algebraic solutions will be accepted. [ 4 ] 2 5. The height of a drone in metres over time in minutes is given by . The height of a second drone in metres over time in minutes is?(?) = 3 − log 2 (? − 1) given by . Determine the time when the two drones will be at?(?) = log 2 ? + log 2 (? + 2) the same height and state the height as well. Only algebraic solutions will be accepted. [ 5 ] C) Thinking/Inquiry [ 4 ] 6. Given that is the base function of the transformed function? ?( ) = 3? ? ?( ) = 81(3)?−2 − 5 a) Create an equation to describe without the use of a vertical stretch.?(?) b) Create an equation to describe without the use of a horizontal translation .?(?) 3 7. If logbn 2 = 5, determine the value of lognb 3. Use laws of logarithms. [ 4 ] D) Communication 8. Given 2 (6 - 2x) + 3?(?) = − 2 log a) Determine the following information; show your calculations. [ 6 ] 2 (6 - 2x) + 3 ?(?) = − 2 log Domain Range x-intercept y-intercept asymptote 4 b) Graph the function. Label all important features for full marks. [ 2 ] 9. Clearly explain, using correct mathematical terminology, the difference(s) between the graph of and [ 2 ]? = ??? 6 ? ? = ??? 6 (36?2) 5