The population P(t) of a culture of bacteria is given by P(t)=-1873t^2+95,000+15000, where t is the time in hours since the culture was started. Determine the time at which the population is at a maximum. Round to the nearest hour.

25 hours.

Step-by-step explanation:

We have been given that the population P(t) of a culture of bacteria is given by ,  where t is the time in hours since the culture was started. We are asked to find the time at which the population is at a maximum.

We can see that our given function is a downward opening parabola, so it maximum point will be vertex. To find the time at which the population is at a maximum, we will find the x-coordinate of parabola.

We know that x-coordinate of a parabola can be found using formula .

Upon rounding our answer to nearest hour, we will get:

Therefore, the population will be maximum at 25 hours.

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