Chapter 8.6, Problem 33E

a.

To determine

To find what type of function represents the numbers of donations collected by organizations A, B, C.

Explanation of Solution

Given:

The organization A quadruples each hour in number of donations and the organization B and C have the following tables and graphs respectively-

  

Calculation:

Organization A has a common ratio of $4$ , so its function is exponential.

Organization B has a common differenceof $4$ , so its function is linear.

Organization C represents parabola so its function is quadratic.

To determine

To find the average rate of change of each function for each 1-hour interval from $t=0$ to $t=6$ .

Explanation of Solution

The average rate of change can be calculated as follows for each function-

Organization A    Organization B    Organization C

From $t=0$ to $t=1$ $\frac{4-1}{1-0}=3$  $\frac{4-0}{1-0}=4$  $\frac{4-0}{1-0}=4$

From $t=1$ to $t=2$ $\frac{16-4}{2-1}=12$  $\frac{8-4}{2-1}=4$  $\frac{16-4}{2-1}=12$

From $t=2$ to $t=3$$\frac{64-16}{3-2}=48$$\frac{12-8}{3-2}=4$$\frac{36-16}{3-2}=20$

From $t=3$ to $t=4$$\frac{256-64}{4-3}=192$$\frac{16-12}{4-3}=4$$\frac{64-36}{4-3}=28$

From $t=4$ to $t=5$$\frac{1024-256}{5-4}=768$$\frac{20-16}{5-4}=4$$\frac{100-64}{5-4}=36$

From $t=5$ to $t=6$$\frac{4096-1024}{6-5}=3072$$\frac{24-20}{6-5}=4$$\frac{144-100}{6-5}=44$

b.

To determine

To find for which function the average rate of change increase most quickly.

Answer to Problem 33E

Organization A

Explanation of Solution

From the part (b) it is clear that for organization A, the average rate of change increase most quickly. The number of donations increases as the number of hours increases.