The maximum time in hours will be equal to 24.64 hours.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given function is P(t) = -1684t² +83000t + 10000
The maximum time will be calculated by differentiating the given function with respect to 't' and equate with zero.
[tex]\dfrac{dP(t)}{dt}[/tex] = -1684t² +83000t + 10000 = 0
[tex]\dfrac{d}{dt}[/tex][-1684t² +83000t + 10000] = 0
-3368t + 83000 = 0
3368t = 83000
t = 24.64 hours
Therefore the maximum time in hours will be equal to 24.64 hours.
The correct question is given below:-
The population p(t) of a culture of the bacterium Pseudomonas aeruginosa is given by,p(t)= -1684t² +83000t + 10000 which is the time in hours since the culture was started. Determine the time the population was at its maximum. Round to the nearest hour.
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