Answer
a) Initially very small, then larger, reaches a maximum and decreases toward $0$
b) $t$ = 8 hours.
c) Concave upward on $(0, 8)$, concave downward on $(8, 18)$
d) Inflection point: $(8, 350)$
Work Step by Step
a) The rate of increase of the population is given by the slope of the tangent to the graph. It is initially very small, then gets larger until it reaches a maximum at about $t$ = $8$ hours, and decreases toward $0$ as the population begins to level off.
b) The rate of increase has its maximum value at $t$ = 8 hours.
c) The population function is concave upward on $(0, 8)$ and concave downward on $(8, 18)$
d) At $t$ = 8, the population is about 350, so the inflection point is about $(8, 350)$
