A bacteriologist doing research on antibiotics has discovered that certain type

Question

A bacteriologist doing research on antibiotics has discovered that certain type of disease causing bacteria can be effectively treated using acocktail of two different antibiotics administered at specific intervals. The population changes in response to the antibiotics according to the function F(t) = -0.0224t^3 + 4.4.5676t^2 - 252.4610t + 5000, where t is in the interval [0, 200]. The maximums of the function correspond to the times when the antibiotics were administered. At what times, t, are the antibiotics administered and what is the population of bacteria at those times?

Explanation / Answer

F(t) = -0.0224t^3 + 4.4.5676t^2 - 252.4610t + 5000

f'(t) =-0.0672t^2+8.913t-252.4610 =0

at t=40.99 and t= 91.63 the antibiotics administered and what is the population of bacteria at those times?

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