ID: A Name: 5. (5 points) The population of frogs in a marsh was recorded for several years. Year 8 Number of Frogs 252 272 290 304 a) Use logarithmic regression to model the data. (Find the equation and write it down.) Round all values to the nearest hundredth. b) Estimate the frog population in the 5th year, Show your work. c) Estimate the frog population in the 12th year. Show your work. 10ID: A Name: 3. (4 points) Aima is sitting in an inner tube in the wave pool. The depth of the water below her, in terms of time, during a series of waves can be represented by the graph shown. 28 24 - 1.6- Height ( 12 0.8 - 0.4 2 3 4 Time (s) From this graph, generate a sinusoidal function which represents the wave cycle in the form: y = asin(he te) ed. The value of c is 1. If necessary, round any values to one decimal place. 4. (5 points) A sandbox has the dimensions 1.2 m by 1.5 m with a height of 0.3 m. While remodelling their backyard, a parent wants to decrease each dimension of the sandbox by the same amount. The following function represents the possible volumes: V(x) = (1.2-x)(1.5-x)(0.3-x), where x is the decrease in dimension. a) Describe the end behavior of the function. b) What is the y intercept? c) What are the x intercepts? d) What is the domain? e) What is the range? 10Name: ID: A 6. (4 points) Bobby kayaks 6 km upstream to see a bridge and then kayaks back downsream to his starting point. It takes him 4 hours in total to complete his trip. IF s trip. If the stream is travelling at a speed of 2 km/h, how fast can Bobby kayak in still waters? The chart below summarizes this information. Let x be Bobby's speed in still waters. distance (lon) speed (lem/h) Time (h) upstream x - 2 6 X - 2 downstream 6 + +2 2 4 2Name: ID: A Problem 1. (3 points) A research company summarized the average time spent everyday by teenagers watching television. Year 1999 2000 2001 2002 2003 14 2005 2006 Time (min) 179 169 195 196 185 182 The above data can be modelled by a quadratic regression function in the form: y = ax + bx +c, where x is the year from 1999 and y is the time in minutes. a) Determine the regression equation. Round decimals to one decimal place, if necessary. b) In which year does the maximum amount of television occur? c) To the nearest minute, how much time spent watching television occurs is 2008? 2. (3 points) The graph of a sinusoidal function is shown. Describe this graph by determining its range, the equation of its midline, and its amplitude. Show your work. -2- 0.1 0.2 03 0,4 0.5 06 0.7 0.8 09 1.0 -4- -6- -8-ID: A Name: Problem 1. (4 points) Which exponential function matches each graph below? Provide your reasoning (Hint: Consider y intercept and whether the graph is increasing decreasing. ) 1) y= 2(3)' ii) v = 3(2) i) V= = (3)' 2. (2 points) An increasing exponential function y = a(b) and a decreasing exponential function y = c(d) intersect at the point (0, 3). Which characteristics of the functions are the same? Which characteristics would be different?Name: ID: A 3. (5 points) The following data table shows the amount of caffeine in Byung's system after drinking a can of cola. Hours 4 6 Caffeine (mg) 46 34 18 a) Using your graphing calculator, create a scatter plot, and find curve of best fit for the data using exponential regression. (Find the equation and write it down.) b) Use your line of best fit to determine how much caffeine was in the can, to the nearest tenth. Explain. c) Use your graph to estimate how many minutes it took for the level of caffeine to reach 50 mg. 4. (4 points) Which function matches each graph below? Provide your reasoning. 1) y = = Inx iii) y =-2 logx if) y = Slogx iv) y = 2(5)* b)ID: A Name: 4. (4 points) Simplify. State any non-permissible values. 2x - 18 x-1 *+3 5. (3 points) Simplify. State any non-permissible values. x + 3x +2 . 3x+6 x - 1 x - 1