Neighboring office buildings are both reporting cases of the flu among their workers. The first cases of the flu in each building occurred on the same day.

Question

The number of cases of the flu in Building 1 is representative of the following function where x is the number of days since the first case of the flu was reported: f(x)=14.25x2+3
The number of cases of the flu in Building 2 is represented by the following graph where x is the number of days since the first case of the flu was reported.

The graph passes through the points (0,3), (1,12), (2,48) and (3,192).

Complete the table below to show how many flu cases there are for each building. (Round your answer to the nearest whole number).

x 0 1 2 3
Building 1
Building 2

Answer 1

To complete the table, we need to evaluate the function \( f(x) = 14.25x^2 + 3 \) for Building 1 for each value of \( x \), and we can extract the values for Building 2 from the points provided in the graph.

Calculating Flu Cases for Building 1:

1. For \( x = 0 \): \[ f(0) = 14.25(0)^2 + 3 = 0 + 3 = 3 \]

2. For \( x = 1 \): \[ f(1) = 14.25(1)^2 + 3 = 14.25 + 3 = 17.25 \approx 17 \]

3. For \( x = 2 \): \[ f(2) = 14.25(2)^2 + 3 = 14.25(4) + 3 = 57 + 3 = 60 \]

4. For \( x = 3 \): \[ f(3) = 14.25(3)^2 + 3 = 14.25(9) + 3 = 128.25 + 3 = 131.25 \approx 131 \]

Values for Building 2:

From the graph points provided:

• For \( x = 0 \): There are 3 cases.
• For \( x = 1 \): There are 12 cases.
• For \( x = 2 \): There are 48 cases.
• For \( x = 3 \): There are 192 cases.

Completed Table:

\[ \begin{array}{|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 \ \hline \text{Building 1} & 3 & 17 & 60 & 131 \ \hline \text{Building 2} & 3 & 12 & 48 & 192 \ \hline \end{array} \]

Thus, the completed table contains the number of flu cases for each building over the specified days.