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October 24, 2014

Homework Help: Math - Derivative of a polynomial function

Posted by Anonymous on Saturday, October 16, 2010 at 6:35am.

The population, p in thousands of bacteria colony can be modelled by the function p(t)=200+20t-t^2, where t is the time, in hours, t is greater than or equal to zero.

a) Determine the growth rate of the bacteria population at each of the following times.
i>3h
ii>8h

Ans: find the 1st derivative which is 20-2t, substitute the times given and it yield a negative number and that in thousands is the answer.

b)What are the implications of the growth rates in part a)

Ans: since the answer are negative they suggest that the population of the bacteria is decreasing.

c)When does the bacteria population stop growing? What is the population at this time.

Ans: set the original equation to zero it will give a time in hours and substitute that time into the first derivative.

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