Question

The number of bacteria after ? hours in a controlled laboratory experiment is ? = ?(?).

a. Describe the meaning of ?′(4) and include right units.

b. If the supply of nutrients is limited, which value do you think is larger ?′(4) or ?′(15)?

Answer 1

(a) : Here, we have two parameters

                                 y= Number of bacteria

                                 t= Time

        so f'(t) usually indicates the slope but the real meaning here for slope is the growth or decay of

        bacteria. Its units are growth or decay of bacteria per an hour

(b) If the supply of nutrients is limited f'(4) will be larger because there will be more growth here.

     for 4 hours, we can say there will be a little amount of nutrients so that the bacteria can grow but

     for 15 hours there will be less nutrients compared to there at 4 hours so the growth is also less.