#### Answer

(a) Over time, the population increases at a faster and faster rate. The slope increases over time until the slope reaches a maximum at the inflection point.
After the inflection point, the slope gradually decreases. This shows that the population is still increasing, but it is increasing at a slower and slower rate.
(b) The rate of population increase is the highest after approximately 8 hours.
(c) The population function is concave upward on the interval $(0,8)$
The population function is concave downward on the interval $(8, 18)$
(d) The inflection point is approximately at the coordinates $(8, 300)$

#### Work Step by Step

(a) Initially, the population increases slowly. Over time, the population increases at a faster and faster rate. We can see that the slope increases over time until the slope reaches a maximum at the inflection point.
After the inflection point, the slope gradually decreases. This shows that the population is still increasing, but it is increasing at a slower and slower rate.
(b) The rate of population increase is the highest when the slope of the graph is a maximum. This occurs after approximately 8 hours.
(c) The population function is concave upward on the interval $(0,8)$
The population function is concave downward on the interval $(8, 18)$
(d) The inflection point is the point on the graph when it changes from concave upward to concave downward. The inflection point is approximately at the coordinates $(8, 300)$