Use the table to answer the question.

Question

x 0 1 2 3 4 5
p(x)
25 50 100 200 400 800
Sandy observes a beetle population in her laboratory. The following table tracks the number of beetles after x weeks. What is the average rate of change in beetles over weeks three to five?

(1 point)
Responses

500 beetles per week
500 beetles per week

600 beetles per week
600 beetles per week

300 beetles per week
300 beetles per week

75 beetles per week

Answer 1

To find the average rate of change in beetles from week 3 to week 5, we first need to determine the number of beetles at those two points in time based on the given values in the table.

From the table:

• At week 3 (x = 3), the number of beetles (p(3)) is 200.
• At week 5 (x = 5), the number of beetles (p(5)) is 800.

Now, we can use the formula for the average rate of change:

\[ \text{Average Rate of Change} = \frac{p(5) - p(3)}{5 - 3} \]

Plugging in the values:

\[ \text{Average Rate of Change} = \frac{800 - 200}{5 - 3} = \frac{600}{2} = 300 \]

Therefore, the average rate of change in beetles over weeks three to five is 300 beetles per week.