Question

The average rate of change from 3 seconds to 7 seconds for EACH?

PLEASE HELP HURRY
SLOPE
GOLF BALL
SECONDS METERS

0 0

3 14

7 32

9 24

12 2

BASEBALL
SECONDS METERS

0 0

3 6

7 15

9 13

12 0

Answer 1

• Golf ball = 4.5, Baseball = 2.25

Explanation:

The average rate of change between two points is the slope of the line between those points.

Golf ball

The points are:

• (3, 14) and (7, 32)

The slope is:

• m = (32 - 14)/(7 - 3) = 18/4 = 4.5

Baseball

The points are:

• (3, 6) and (7, 15)

The slope is:

• m = (15 - 6)/(7 - 3) = 9/4 = 2.25

Answer 2

`\textsf{Average rate of change of the golf ball}=(9)/(2)\; \sf m/s`

`\textsf{Average rate of change of the baseball}=(9)/(4)\; \sf m/s`

Explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

`\boxed{(f(b)-f(a))/(b-a)}`

To find the average rate of change from 3 to 7 seconds:

• a = 3
• b = 7

Therefore, use the formula:

`\implies (f(7)-f(3))/(7-3)`

Golf Ball

`\begin{array}c\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&14\\\cline{1-2} 7&32\\\cline{1-2} 9&24\\\cline{1-2} 12&2\\\cline{1-2}\end{array}`

From inspection of the table:

• f(3) = 14
• f(7) = 32

Substitute these values into the formula to find the average rate of change of the golf ball from 3 seconds to 7 seconds:

`\implies \textsf{Average Rate of Change}=(f(7)-f(3))/(7-3)=(32-14)/(7-3)=(9)/(2)\; \sf m/s`

Baseball

`\begin{array}c\cline{1-2} \sf Seconds & \sf Meters \\\cline{1-2} 0&0\\\cline{1-2} 3&6\\\cline{1-2} 7&15\\\cline{1-2} 9&13\\\cline{1-2} 12&0\\\cline{1-2}\end{array}`

From inspection of the table:

• f(3) = 6
• f(7) = 15

Substitute these values into the formula to find the average rate of change of the baseball from 3 seconds to 7 seconds:

`\implies \textsf{Average Rate of Change}=(f(7)-f(3))/(7-3)=(15-6)/(7-3)=(9)/(4)\; \sf m/s`