## Calculus: Early Transcendentals 8th Edition

(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 $(8, 300)$
(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 $(8, 300)$