Question

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

Answer 1

Answer:

The average rate of change over the interval [9,10] is greater than that over the interval [5,8] by 6490.

Step-by-step explanation:

The value of f(x) = 4052 for x = 9 and f(x) = 11014 for x = 10.

Therefore, the average rate of change of f(x) with respect to x over the interval [9,10] is given by  

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{11014 - 4052}{10 - 9} = 6962$

Now, the value of f(x) = 75 for x = 5 and f(x) = 1491 for x = 8.

Therefore, the average rate of change of f(x) with respect to x over the interval [5,8] is given by

= $\frac{\textrm {Total change in value of f(x)}}{\textrm {Total change in value of x}}$

= $\frac{1491 - 75}{8 - 5} = 472$

Therefore, the average rate of change over the interval [9,10] is greater than that over the interval [5,8] by (6962 - 472) = 6490. (Answer)