4. The number of new cases per day of an infectious disease can be (not so accurately) modeled by the function 1000 n(t) = -t/14 + et/14 where t represents the number of days before or after the peak of new cases per day. (a) Use graphing software to help you sketch this function on the interval t = -28 to t = 28. Label your axes, including units. (b) Use a right-handed Riemann sum with three rectangles to estimate the number of new cases in the one week span, from two weeks to one week prior to the peak. Visualize this Riemann sum on your plot. Is this an over-estimate or under-estimate of the true area under the curve? Use a calculator to get a numerical estimate here. (c) Use a right-handed Riemann sum with three rectangles to estimate total new cases in the week ending at the peak (t = 0). How does this compare in size to the prior one-week estimate of new cases you found above? Use a calculator to get a numerical estimate here. (d) Use yet another right-handed Riemann sum with three rectangles to estimate in the week-long span beginning two weeks after the peak. In this case, is this an over-estimate or under-estimate of the true area? Use a calculator to get a numerical estimate here