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The number of bacteria in a culture is given by the function [tex]n(t) = 940 e^{0.45t}[/tex], where [tex]t[/tex] is measured in hours.

What is the continuous rate of growth of this bacterium population?

Answer :

Final answer:

The continuous rate of growth of the bacterium population is dn/dt = 423e^(0.45t), found by taking the derivative of the population function with respect to time.

Explanation:

The continuous rate of growth of the bacterium population can be found by taking the derivative of the population function with respect to time. In this case, the derivative of n(t) = 940e^(0.45t) is dn/dt = 423e^(0.45t). The continuous rate of growth is given by the derivative dn/dt, which represents the slope of the population curve at a particular time.

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