Final answer:
The ant farm expands at a rate of 3 square inches per month, making the constant of proportionality 3. The size in month 7 is 24 square inches, not 21 or 28 as stated in the options. Options 3 is true, while Options 1, 2, 4, and 5 are incorrect.
Step-by-step explanation:
You're asking about the rate of expansion of Kelly's ant farm based on the given data for certain months. To determine the correct constant of proportionality and the size of the ant farm in month 7, we first need to analyze the rate at which the ant farm is expanding based on the information provided for month 3 and month 13.
The size of the ant farm in month 3 is 12 square inches, and in month 13 it is 42 square inches. To find the rate of expansion per month, we'll subtract the size of the farm in month 3 from the size in month 13 and then divide by the difference in months:
Rate = (Size in month 13 - Size in month 3) / (Month 13 - Month 3)
Rate = (42 - 12) / (13 - 3)
Rate = 30 / 10
Rate = 3 square inches per month
Therefore, the constant of proportionality is 3, meaning Kelly's ant farm expands by 3 square inches each month. Now, we can find the size of the ant farm in month 7 by multiplying the rate by the number of months, starting from month 3.
Size in month 7 = Size in month 3 + (Rate × (Month 7 - Month 3))
Size in month 7 = 12 + (3 × (7 - 3))
Size in month 7 = 12 + (3 × 4)
Size in month 7 = 12 + 12
Size in month 7 = 24 square inches
So, the statement in Option 1 is incorrect, and the statement in Option 2 is also incorrect. Option 3 is true because it correctly identifies the rate of expansion (constant of proportionality) as 3 square inches per month, not 4. Therefore, Option 4 is incorrect as it wrongly states the rate as 15 square inches per month. Lastly, since we just calculated the rate to be 3, not 4, Option 5 is incorrect because the equation s = 4m does not accurately represent the growth of Kelly's ant farm.