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Interpreting the Derivative in Context
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The number of bacteria in a culture is modeled by the differentiable function $$ B(t) $$, where $$ t $$ is the time in hours since the culture was started and $$ B(t) $$ represents the number of bacteria. Which of the following is the best interpretation of $$ B'(6) = 450 $$?

A

Over the time interval $$ 0 \le t \le 6 $$ hours, the bacteria population increased by 450 bacteria.

B

Over the time interval $$ 0 \le t \le 6 $$ hours, the average rate of bacteria growth is 450 bacteria per hour.

C

At time $$ t = 6 $$ hours, the bacteria population is growing at a rate of 450 bacteria per hour.

D

At time $$ t = 6 $$ hours, the rate at which the bacteria population grows is increasing at a rate of 450 bacteria per hour per hour.

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