Problem 1. The velocity of a particle f(t) (in m/s, moving East) for some values of time is recorded in the table below. Assume f(t) is always increasing. is 8 1012141618 20 22 24 26 28) f(t) -42 40 -38 -33 31 -27 25 20 15 12 Si A. Use a left Riemann sum with n = 3 to approximate the displacement of the particle over the interval [14, 32]. Be sure to include appropriate units. B. Ron estimates that the actual displacement of the particle is 600 meters West between 14 and 32 seconds. Please select a response below and briefly explain. L Ron is definitely correct. ll. Ron is possibly correct. lll. Ron is definitely incorrect. 33 7m d 1'\" 2 Problem 2. Evaluate the expressiond / 6' dt Problem 3. Consider a continuous function f(t) over the interval [767 6]. You are given that ff fog) dt = _20 and that jg: t) dt = 14. If f(t) is an even function, find 1'02 t) dt. Problem 4. Find the finite area between the curves y = y = m + 6 and the :r-axis. Problem 5. An antibacterial agent is applied to a bacterial colony. The population of a bacterial colony PU) (in millions of organisms) changes at a rate r05) = (4000): _ 8000)e_t2_4t (in millions of organisms per minute) where t refers to the number of minutes after the agent is applied. Right before the agent is applied, the bacterial colony has 2020 million organisms. A. Compute the following expression. If necessary, please round to two decimal points. 1 2020+ f r(t)dt 0 B. Explain the meaning of the expression 2020 + fol rpm dt in context of the problem. C. Your buddy Ron states "As time goes on forever, we expect the bacteria population to go to 0." State whether Ron is CORRECT or INCORRECT and briefly explain your selection