1. Suppose that P(t) = 25(2): 5: + 7 represents the population (in colonies) of bacteria in a culture t hours after an experimental nutritive substance is added to the culture. Evaluate and interpret P(3) and P'(3), using complete sentences. 2. Find the derivative of each function. Perform reasonable simplifications: a. 3(t) = ef tant + 7:5 b. 909) = 1/5- CSCP c. f(x) = 8x5 secx d. s(t) = - t2 Int 3. Suppose we are given the following table of values for r(x), q(x), r'(x), and q'(x). X 1 2 3 4 5 6 7 8 9 -1 6 7 -3 -1 -2 100 r(x) -5 q(x) 5 -1 0 -6 -9 -8 3 r' (x) -10 2 -5 10 9 q'(x) -8 5 -6 2 7 9 0 -9 -2 a. If f (x) = x3r(x), evaluate f'(5) b. If h (x) = ~ r(x) x.q(x)' evaluate h' (3)