Question

select the correct answer from each drop - down menu. a school club will be competing at a state championship and has been working to raise money for the clubs travel expenses. the table shows the amount of money raised each month over a nine - month period beginning in august.
month 1 2 3 4 5 6 7 8 9
amount ($) 250 275 325 300 350 375 375 350 350
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.
claras function: $y=-3.14x^{2}+44.7x + 203.6$
michaels function: $y = 44.64sqrt{x + 1}+246.5$
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 claras function, it would expect the amount of money to
if the club uses michaels function, it would expect the amount of money to each month

Explanation:

Step1: Analyze Clara's function $y = - 3.14x^{2}+44.7x + 203.6$

This is a quadratic function with $a=-3.14<0$. The graph of a quadratic function $y = ax^{2}+bx + c$ is a parabola. When $a < 0$, the parabola opens down - ward. So, as $x$ (representing the month) increases, the value of $y$ (amount of money) will decrease.

Step2: Analyze Michael's function $y = 44.64\sqrt{x + 1}+246.5$

The square - root function $y=\sqrt{x}$ is an increasing function. In the function $y = 44.64\sqrt{x + 1}+246.5$, as $x$ (representing the month) increases, the value of $\sqrt{x + 1}$ increases. Since the coefficient of $\sqrt{x + 1}$ is positive ($44.64>0$), the value of $y$ (amount of money) will increase.

Answer:

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.