8. The pH of a solution can be determined using the formula ph = - log [N* ], where His the hydrogen ion concentration in the solution. a. The hydrogen ion concentration of a particular brand of fruit juice is 0.0003 mol/L. Determine the p/ of the solution, to the nearest tenth. (1 mark) Page 8 of 12 Vista Virtual School - A5-8 b. A tomato has a pl of 3.0. Algebraically determine the hydrogen ion concentration of this solution. (2 marks)9. Match the expanded logarithmic expression in the left column with the simplified form of the expression in the right column. (3 marks - 0.5 marks each) Expanded Form Simplified Form A. loga B + loga C i. logs ( *) b. log- A - loge B ii. loge () c. log, A + Mlog, B iii. loge A d. log,A - log, M + log. C iv. log, (ABC) logy A C. v. loga ( BC) logMC f. logBA + log, B + log, C vi. log, (ABM) b. C. d. e. f.10. Solve the following logarithmic equations algebraically. Express your answers to the nearest hundredth, if necessary. (4 marks - 1 mark each) a. log x = 6 b. logx 64 = 3 c. log2 12 = x d. logs 5* = -3 11. Solve each equation below algebraically (using logarithms), and graphically (using technology). If necessary, round your answer to the nearest hundredth. a. 6x -1 = 12 Algebraically (2 marks) Graphically (2 marks) Graph y, = Graph yz = Coordinates of intersection: Solution: x = Page 10 of 12 Vista Virtual School - A5-8 b. 331 = 2x+2 Algebraically (2 marks) Graphically (2 marks) Graph y1 = Graph yz = Coordinates of intersection: Solution: x =12. Analyze the given function equations then complete the table by determining the following characteristics of each function. (8 marks) Equation Amplitude Period Horizontal Midline Translation y = sin( x + 2) + 0.5 y = 0.25 sin 2 (x + 45) - 1 y = 4 sin 0.5 (x - 1) y = 5.4 sin 0.75 (x - 90) - 4 Page 11 of 12 VVS: 30-2 A5-8 (May. 2022) 13. Analyze each graph then state the amplitude, period, equation of the midline and the corresponding sinusoidal equation. (10 marks) The starting point of each sine carve is marked with a square. WINDOW Graphs were drawn on a TI calculator in degree mode with window settings of. Xmin= =90 Xmax=360 Xsc1=30 Ymin= -2 Ymax=4 Yscl=1 Amplitude: Period: Midline: Equation: Amplitude: Period: Midline: Equation Amplitude: Period: Midline: Equation Amplitude: Period: Midline: Equation14. The motion of a passenger on a Ferris Wheel is periodic. The passenger starts in the lowest position then rises to the maximum height and returns to the lowest position. This motion repeats as the wheel rotates. The Ferris Wheel to the right has a diameter of 50 m. Passengers enter and exit the riding capsules on a platform that is I'm above the ground. It takes 10 minutes for the Ferris Wheel to complete I full revolution. a. Sketch a sinusoidal graph that models the height of a passenger above the ground for 2 revolutions. Choose an appropriate scale that uses more than half of the provided grid. Label your axes, y-intercept, amplitude, period and midline on your graph. (3 marks) b. Model the function above with an equation of the form h = a sin (bt - 1.57) + d, where h represents the height, in metres, of a passenger above the ground, and t represents the time, in minutes, after the ride has started. Express the values of a, b, and d to the nearest hundredth, if necessary. (1 mark) End of Assignment