Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

The table of values represents a polynomial function ​f(x).

How much greater is the average rate of change over the interval [7, 9] than the interval ​ [4, 6] ​ ?

Answer 1

Answer: 603

Explanation:

Average rate of change is the slope
`m=(y_2-y_1)/(x_2-x_1)` over the given interval.

Interval [7, 9] is between x = 7 and x = 9. Use the table to see that the coordinates are (7, 1852) and (9, 3878). Then use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(3878-1852)/(9-7)\\\\.\quad =(2026)/(2)\\\\.\quad = 1013`

Interval [4, 6] is between x = 4 and x = 6. Use the table to see that the coordinates are (4, 358) and (6, 1178). Then use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(1178-358)/(6-4)\\\\.\quad =(820)/(2)\\\\.\quad = 410`

Next, find the difference between the slopes above:

[7, 9] - [4, 6]

= 1013 - 410

= 603