Please answer all questions, so I can check the answers I handed in.

Question 3 (16 marks) a. A leak of oil from an underwater well forms an "oil slick" on the water surface in the form of a circle. The radius of the slick is increasing at a rate of 2.5 metres per minute. Formulate an expression for the rate of increase of the circumference of the oil slick and from this determine the rate of increase of the circumference of the slick when the radius of the slick is 50 metres. (Be sure to show the units of measurement) (4 marks) b. Consider the function f (x) = x - ex + 2. This function has a positive root which we would like to approximate. i. Evaluate f(0), f(1) and f (2), each to 3 decimal places. (2 marks) ii. Make a statement about the position of the root in relation to the values used in part i. and explain the reasoning that led to this conclusion. (2 marks) iii. Perform a single iteration of Newton's Method (using x = 1 as an initial approximation) to get a better approximation for the root in question. (2 marks) c. The concentration (C) of a naturally occurring chemical in the bloodstream of a person infused with a specific quantity of this chemical is modelled by the formula C(t) = 100 + 120e-0.5 where C is the concentration (in parts per million) and t is the time elapsed (in minutes) after infusion. i. Determine the rate of change of the concentration of the chemical at t = 2 minutes. (3 marks) ii. Determine the average concentration of the chemical in the bloodstream of the person during the period t =0 to t = 10.