Question

What is the average rate of change for this exponential function for the

interval from x=2 to x= 4?
a.-6.
b.6
c.12
d.-12​

Answer 1

The correct answer is:

b. 6

Explanation:

We are given the graph of an exponential function.

We have to find the average rate of change for this exponential function from x = 2 to x = 4.

First of all, let us plot the point on the graph on the points x = 2 and x = 4.

Please refer to the attached diagram.

We can easily find that the value of y at x = 2 is 4.

the value of y at x = 4 is 16.

`\therefore` the coordinates are (2, 4) and (4, 16).

Let the points be A(2, 4) and B(4, 16)

Now, let us find the average rate of change for exponential function i.e. change in value of y divided by change in value of x from x = 2 to x = 4:

Formula:

`\text{Average rate of change = } \frac{\text{Change in y coordinate}}{\text{Change in x coordinate}}`

`\Rightarrow (16-4)/(4-2)\\\Rightarrow (12)/(2)\\\Rightarrow 6`

So, correct answer is option b. 6