Names ID: A 3. (4 points) Kira 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. 24 7 eight (m) 23 4 5 Time (s) From this graph, generate a sinusoidal function which represents the wave cycle in the form: y masin(bx +c) +d. 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: P(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? ") What are the x intercepts? d) What is the domain? e) What is the range? 10Name: 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 2004 2005 2006 Time (min) 179 195 196 190 187 185 The above data can be modelled by a quadratic regression function in the form: y = ax + br + 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. 0.1 0.2 03 0.4 05 06 0.7 0.8 09 1.0Name: ID: A 4. (6 points) Consider the equation: 8'=16+3 a) Solve this equation algebraically using logarithms. b) Solve this equation using a rewriting each power to the same base. 5. (4 points) A student borrows $10 000 at an interest rate of 4% per annum, compounded monthly. a) If the student pays the loan off in 10 years, how much does the student pay in interest? b) If the entire loan costs the student $20 000 to pay back, how many years was the loan for