UNIT 3 - ASSIGNMENT EXPONENTIAL & LOGARITHMIC FUNCTIONS TOTAL MARK /30 Instructions: Show all work for full marks. Add space if you need to. Submit ONE FILE (PDF) under Unit 3 Assignment Folder in BrightSpace. 1) The height of a drone in metres over time in minutes is given by f(x) = 3 - log ,(x - 1). The height of a second drone in metres over time in minutes is given by g(x) = log x + log , (x + 2). (Only algebraic solutions will be accepted. Include a final statement) a) Determine the time when the two drones will be at the same height. [4] b) Determine the height of the two drones at the time found in a) [1]2) A singer is performing to a crowd. How many times more intense is her singing at 70 dB, compared to a bird whose call is 34 035'? Show ALL work and include a final statement. Round to one decimal place, if necessary. [4] 3) Given f(x) 2 3:092 (4 - 2x) + 1 3) Determine the following information; show all steps. [6] yintercept asymptote {XI-8) Find the value ofx b) Graph the function. Label all important features for full marks. [2] 4) Write an equation for a logarithmic function with a vertical compression, 3 horizontal stretch, a reflection on x axis, a vertical asymptote x10, and a vertical translation. Explain how your equation satisfies the constraints above using terminology learned in this unit. [5] log 5 ) If 2 ) = (log.x + logy) , where r > 0, y > 0, show that ' ty = 2ry [3 ] 6) One yeast colony of 200 cells is growing exponentially by 10% / hour. Another yeast colony of 1000 cells is diseased and its population is decreasing by 20% / hour. At what time (if any) will the two colonies have the same population? (Only algebraic solutions will be accepted. Include a final statement.) [5]