To determine the correct answers, let's use the given functions and the results for each next month - 10, 11, and 12.
### Clara's Function Results:
Clara's function is given as:
[tex]\[ y = -3.14x^2 + 44.7x + 203.6 \][/tex]
- For month 10:
[tex]\[ y = -3.14(10)^2 + 44.7(10) + 203.6 = 336.6 \][/tex]
- For month 11:
[tex]\[ y = -3.14(11)^2 + 44.7(11) + 203.6 = 315.36 \][/tex]
- For month 12:
[tex]\[ y = -3.14(12)^2 + 44.7(12) + 203.6 = 287.84 \][/tex]
### Michael's Function Results:
Michael's function is given as:
[tex]\[ y = 44.64 \sqrt{x + 1} + 246.5 \][/tex]
- For month 10:
[tex]\[ y = 44.64 \sqrt{10 + 1} + 246.5 = 394.55 \][/tex]
- For month 11:
[tex]\[ y = 44.64 \sqrt{11 + 1} + 246.5 = 401.14 \][/tex]
- For month 12:
[tex]\[ y = 44.64 \sqrt{12 + 1} + 246.5 = 407.45 \][/tex]
### Analysis and Conclusion:
1. Clara's function appears to show a decreasing trend in the amount of money raised each month. The expected amounts (336.6, 315.36, and 287.84) indicate a decline as the months progress.
2. Michael's function shows a slightly increasing trend in the money raised each month, with values being (394.55, 401.14, and 407.45).
Therefore, we can fill in the blanks as follows:
If the club uses Clara's function, it would expect the amount of money to decrease each month.
If the club uses Michael's function, it would expect the amount of money to increase each month.
