A bacteria culture is grown in a petri dish. The table gives the area of the culture, in square centimeters, at various times, in hours, since the beginning of an experiment. The area of the bacteria culture is proportional to the actual number of bacteria in the culture.

The area of the bacteria culture can be modeled by the function
C
given by
C
(
t
)
=
a
b
t
, where
C

(
t
)
is the area, in square centimeters, at time
t
hours since the beginning of the experiment.

Question
Part B

(i) Use the given data to find the average rate of change of the area, in square centimeters per hour, from
t
=
0
to
t
=
2
hours. Express your answer as a fraction or decimal. Show the computations that lead to your answer.

(ii) Interpret the meaning of your answer from (i) in the context of the problem.

(iii) Use the average rate of change found in (i) to estimate the area of the bacteria culture, in square centimeters, at time
t
=
3
hours. Show the work that leads to your answer.