Question 12

The average rate of change per month in the student's account is $52.

The average rate of change per month is calculated by taking the difference in the account balances and dividing it by the number of months over which the change occurred. In this case, the balance increased by $310 over a period of 5 months, resulting in an average change of $62 per month.

A) $290

Option A is incorrect because it represents the total change in the account balance but does not account for the number of months over which this change occurred. The average rate of change must be calculated by dividing the total change by the number of months, which is not reflected in this option.

B) $310

Option B is also incorrect. While $310 is the total increase in the account balance, it does not represent the average monthly change. To find the average, one must divide this total by the 5-month period, leading to a different average rate of change.

C) $621

Option C is incorrect as it significantly overestimates the average rate of change. The figure of $621 does not relate to the actual changes in the savings account and misrepresents the calculations needed to find the average monthly change.

D) $52

Option D is the correct answer. The total increase in the account balance was $310 over 5 months, resulting in an average rate of change of $62 per month. This option accurately reflects the calculation needed to determine the average change per month.

Conclusion

The correct answer, $52, accurately represents the average rate of change per month based on the total change in the student's account balance over the specified period. Options A, B, and C either misrepresent the total change or fail to account for the time frame, leading to incorrect conclusions. Thus, D is the only choice that reflects the proper calculation method for average rate of change.