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gayaneshka [121]
3 years ago
7

The table below shows the number of tadpoles in a pond after a certain number of months.

Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0
<h3>Answer:   Choice D)  6 months to 10 months</h3>

===================================================

Explanation:

  • x = number of months
  • y = number of tadpoles

Highlight the rows that correspond to 6 months and 10 months.

This leads to the two points (6,330) and (10,460).

Apply the slope formula. This is because the slope is the average rate of change.

m = (y2-y1)/(x2-x1)

m = (460-330)/(10-6)

m = 130/4

m = 32.5

This is the average rate of change from month 6 to month 10.

Let A = 32.5 so we can compare it later.

---------------------------

Now let's focus on months 4 and 8

We get the two points (4, 300) and (8, 410)

Use the slope formula again

m = (y2-y1)/(x2-x1)

m = (410-300)/(8-4)

m = 110/4

m = 27.5

Let B = 27.5

--------------------------

For the third answer choice, we have the points (2,240) and (8,410)

Once again, use the slope formula.

m = (y2-y1)/(x2-x1)

m = (410-240)/(8-2)

m = 170/6

m = 28.33 approximately

Let C = 28.33

--------------------------

Lastly for choice D we have the points (4,300) and (10,460)

So,

m = (y2-y1)/(x2-x1)

m = (460-300)/(10-4)

m = 160/6

m = 26.67 approximately

Let D = 26.67

--------------------------

To recap everything, we found these four average rates of change for choices A through D

  • A = 32.5
  • B = 27.5
  • C = 28.33 (approximate)
  • D = 26.67 (approximate)

We see that A is the largest of that group. Therefore, the greatest average rate of change of that group is from month 6 to month 10. This is why <u>choice A</u> is the final answer.

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