Integrals continued/ applications of integrals

Due: Tuesday, March 29th at 5:00pm 1. Determine the area bounded by the following curves: (a) y = 12 - x2 and y = 2 - 6 (b) y = z, y = x, and y = 4x, x 20 2. Let P(t) denote the number of bacteria present in a population at time t. Suppose that the rate at which the population of bacteria grows is given by P' (t) = 200e2t + 50et bacteria per hour. Approximately how many bacteria does the population gain during the first 2 hours? 3. A company's marginal revenue is given by R'(2) = -6x2+ 70x+180 and the marginal cost is given by C'(x) = 20x + 80 where x is the number of items produced. (a) What is the production level that will maximize profit? (b) What is the maximized profit