3. The amount of active ingredient of medicine ingested by the body, A, in milligrams, is a function of time, t, in hours, A(!) = =(121-12) given by (a) Determine the average rate of change of the amount of medicine ingested from (i) 3 hours to 5 hours (ii) 5 hours to 7 hours Compare the two rates with respect to the given information. (3 marks) (b) Estimate the instantaneous rate of change at t = 2 hours. Use an interval of 0.01. Round your answer to the nearest hundredth. Do not find the instantaneous rate of change using the difference quotient or any Calculus method. Explain what the value represents in this situation. (2 marks)4. The student council of a school is selling t-shirts to raise money for their school. The cost to purchase t-shirts from the manufacturer is $200 for the order and $5 per t-shirt. The student council sells the t-shirts for $15 each. (a) Let R represent Revenue, Let C represents cost, and let t represents the number of t-shirts. Determine an equation for R() and C() (2 mark) (b) Create a combined function expressing the profit the council will earn as a function of number of t shirts sold. (1 mark) (c) Determine the number of t-shirts the student council needs to sell in order to break-even. (2 marks)5. Find an expression for ) = / (K) if 3x -y -2=0, 3-x+ 2 =0, and 3k -1 -2 =0 (3 marks) 6. A circle has radius, r, and circumference C. Suppose the area of the circle is given by A, determine an equation for A(r(C)) . (2 marks) 7. Let f(x) = 3x +5 and h(x) = 3x2 +3.x +2 (a) Find a function, g, such that fog = h. Show algebraically that (f o g)(x) = h(x). (2 marks) (b) Determine the value of 8(/(-1)) . (1 mark)1. Describe two instances where an instantaneous rate of change can equal zero. Give an example of a function that illustrates each instance. (3 marks) 2. f(x) = - 1 (a) Given x -4 and g() = sin *, identify the steps you would take to determine the range of (f o g)(x). What is the range of (f o g)(x)? (3 marks) (b) Would the domain of (f o g)(x) be the same as the domain of (go f)(x) be the same? Explain. (2 marks)