   # Math 112 Solutions for 2.1, p.100

1.
(a) 8; 14.4; 15.84. (b) about 16.

(c) -32 ft/sec, -24 ft/sec, -17.6 ft/sec, -16.8 ft/sec

2.
(a)19.67; 19.74; 19.79. (b) about 19.8.

4.
$96.58 per year,$94.67 per year, $93.18 per year. At , the rate of change is about$92.81 per year, which is about 7.92% of . , so this is compounding 4 times per year at 8%.

5.
(a) 25.66, 36.8; 3.47, 4.98; 0.47, 0.67. (b) about 40; about 6; about 1. [Actual: 40.6, 5.49, 0.74.] (c) The velocity will approach 150 and acceleration will approach 0.

8.
The slope at is about -1. No tangent line exists at 1 or at -1.

9.
The slope at is about -2. No tangent line exists at -1 or at 2.

12.
(a) 8.1, 25.5, and 16.8 people per year. The last is indeed the average of the first two.

(c) about 16.8 people per year (using the average growth rate over [1960, 1980]).

(d) 1980: Use the average for [1970, 1990], which is 31.6 people per year.

1990: Use the average for [1980, 2000], which is 49.25 people per year.

13.
If , then if and only if . Hence the result, upon substitution.

14.
If , then and if and only if . Hence, by substitution, .

16.
(a) The slope of is , which is the rate of change.

(b) .   