Math 112 Solutions for 4.3, p. 340

3.
.
5.
6.
. weeks.
7.
years.
8.
(a) moles. (b) about 218.9 million years.
11.
minutes.
13.
(b) . (c) The graph of is increasing where is positive, concave upward where is increasing, and concave downward where is decreasing. Thus the graph of is always increasing, concave upward between and , and concave downward between and .

15.
Use , , and the condition when . When , 99.98%.

16.
hours.
17.
The rate of increase begins to decrease between 1983 and 1984, so half capacity is about 1900, making the carrying capacity about 3800.
18.
(a) . (b) . (c) . (d) . (e) ... an essay summarizing (a) - (d)...
19.
(a) F. (b) Using the same , F. (c) about 35.12 minutes.
20.
(a) Show that , so that is constant; find .

(b) Show that , so that is constant; then show that . The sum of squares is zero only if each square is zero.