The population P(t) of a culture of bacteria is given by P(t) = -1,840t2 + 81,000t + 10,000, 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.

The population is at a maximum after 22 hours.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

It's vertex is the point

In which

If a<0, the vertex is a maximum point, that is, the maximum value happens at , and it's value is

In this question:

Determine the time at which the population is at a maximum.

This is the value of t at the vertex.

We have that . So

The population is at a maximum after 22 hours.

point a is the center of this circle.

the ratio of the lengths of (ef/bc) and (ad/ih) is 2: 1.

step-by-step explanation:

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step-by-step explanati∵∵∴∴on: