Question

modeling data with functions: mastery test
1
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 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 next three months.
claras function: y = - 3.14x^2+44.7x + 203.6
michaels function: y = 44.64√(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 drop - down each month.
if the club uses michaels function, it would expect the amount of money to drop - down each month.
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Explanation:

Step1: Analyze Clara's function

Clara's function is a quadratic function $y = - 3.14x^{2}+44.7x + 203.6$. The coefficient of $x^{2}$ is $a=-3.14<0$, so the graph of the quadratic - function is a parabola opening downwards. As $x$ (representing the month) increases, the value of $y$ (amount of money) will eventually decrease.

Step2: Analyze Michael's function

Michael's function is $y = 44.64\sqrt{x + 1}+246.5$. The square - root function $\sqrt{x+1}$ is an increasing function. As $x$ (representing the month) increases, the value of $\sqrt{x + 1}$ increases, and 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.