Interpreting the Derivative in Context
The number of bacteria in a culture is modeled by a differentiable function $$B(t)$$, where $$t$$ is the time in hours. Which of the following is the best interpretation of $$B'(6) = 450$$?
A
At time $$ t = 6 $$ hours, the bacteria population is growing at a rate of 450 bacteria per hour.
B
Over the time interval $$ 0 \le t \le 6 $$ hours, the bacteria population increased by 450 bacteria.
C
Over the time interval $$ 0 \le t \le 6 $$ hours, the average rate of bacteria growth is 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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