Question: An epidemiologist working for a healthcare facility was tracking a short-lived outbreak of influenza, which she modeled with the following function, \(f\left( t \right)=18{{t}^{2}}-2{{t}^{3}}\), to determine the number of new cases reported daily; the independent variable, t, represents the number of days into the outbreak. How many new cases were reported on the (a) second day, (b) fourth day, and (c) eighth day? (d) This outbreak lasted for how many days? [COMMENTS & HINTS: An outbreak ends when the number of new cases reported daily returns to zero.] (e) On what day did the number of reported cases peak, or reach a maximum? [COMMENTS & HINTS: Use calculus methods to explain your answer.] (f) How many new patient cases were reported on that day? (g) Affirm that this extreme point is indeed a maximum for this function. [COMMENTS & HINTS: Use calculus methods to confirm the concavity of the graph at this point.] (h) On what day did the rate of change in the number of reported new patient cases begin to level off? [COMMENTS & HINTS: Use calculus methods. This does not refer to an extreme point, but rather a point of inflection.]