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A school club will be competing at a state championship and has been working to raise money for the club's travel expenses. The table shows the amount of money raised each month over a nine-month period beginning in August.

\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline Month & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline Amount ( [tex]$)$[/tex] & 250 & 275 & 325 & 300 & 350 & 375 & 375 & 350 & 350 \\
\hline
\end{tabular}

Based on the data in the table, Clara and Michael each use their own function to determine the amount of money the club should expect to raise in the next three months.

Clara's function: [tex]$y = -3.14x^2 + 44.7x + 203.6$[/tex]
Michael's function: [tex]$y = 44.64 \sqrt{x+1} + 246.5$[/tex]

How does using the different models affect the amount of money the club would expect to raise in the next three months?

If the club uses Clara's function, it would expect the amount of money to [tex]$\square$[/tex] each month.

If the club uses Michael's function, it would expect the amount of money to [tex]$\square$[/tex] each month.

Sagot :

GinnyAnswer
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.
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