11. The population of a certain city is growing exponentially. The population was 112,000 in 2014, and the observed doubling time for the population is 18 years. In what year will the population reach 500,000? /8 marks) 12. Find the equation of the straight line that travels through the point (x,y) = (-3,1) and is perpendicular to the line y = 2x + 1. /6 marks)\f2. A rectangular pasture is twice as long as it is wide. The area of the pasture is 115,200 fil. What are the dimensions of the pasture? (6 marks) 3. The resident population of South Carolina (in thousands) was 4024 in the year 2000 and 4255 in the year 2005. Assume that the relationship between the population (y) and the year (t) is linear. Let t=0 represent the year 2000. (10 marks] a) Determine the equation for the linear model (function) for the data. b) Use the equation to predict the population in 2022.4. /8 marks) 4 a) Find and state the domain of the function / (x) =- V5- 3x by If f(x) = x + 2x, evaluate and simplify the expression for [(x+ 1)- f(1) 5 . Consider the graph of the function Now sketch the graph of the function y = f (x) shown here: y=2f(x+1)-1 (6 marks]6. A toy rocket is launched from the roof of a 76 metre tall building. The rocket's height, in metres, as a function of time, in seconds, is given by (() = 76 + 281 - 472. [12 marks] a) After how many seconds will the rocket hit the ground? b) At what time does the rocket reach its highest point. What is this maximum height? c) Use the above information to sketch a careful (and labelled) graph of the rocket's height as a function of time.8. Use the law of logarithms to calculate the precise value of: (6 marks) a) log, 60-log, 15 b) - -log, 27 9. A bacteria culture initially has 10 bacteria and is observed to double every 1.5 hours. (10 marks) a) Find the exponential model equation for the number of bacteria in the culture after t hours. b) Find the number of bacteria after 3.5 hours. c) After how many hours will the bacteria count reach 10,000?10. State the equation of a circle with centre (x, )) = (-1,2) and radius . /2 marks) Answer. 11. (4 marks] a) Convert 5 radians to exact degree measure. Answer: b) Convert 165" to exact radian measure. Answer: 12. The right triangle below has one side and one other angle given. Find the measure of the remaining angle x as well as the length of the remaining two sides a and b. Note that the diagram may not be drawn to scale. (6 marks) 6 30" X = 1 = b=