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Answer :
The date when the number of new flu cases was increasing at a rate of 160 cases/day is December 14th, determined by finding the first derivative of the given model and solving for the day. The correct option is [C] December 14th.
To find on what date the number of new flu cases was increasing at a rate of 160 cases/day, we need to find the rate of change of the function that models the number of new cases.
The given model is f(t) = 5t^2 + 20t, where t represents the day of the month.
The rate of change is given by the first derivative of the function with respect to time, which is f'(t) = 10t + 20. Setting this equal to 160, we get 10t + 20 = 160. Solving for t gives t = 14.
Thus, on December 14th, the rate of new flu cases was 160 cases per day. Therefore The correct option is [C] December 14th.
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