Question

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.

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 calculate the number of flu cases for Building 1 using the given function \( f(x) = 14.25x^2 + 3 \) and extract the values for Building 2 from the provided graph points.

### Building 1 Calculation:

Using the function \( f(x) = 14.25x^2 + 3 \):

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

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

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

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

### Building 2 Values:

The values from the graph points are as follows:

- For \( x = 0 \): \( 3 \)
- For \( x = 1 \): \( 12 \)
- For \( x = 2 \): \( 48 \)
- For \( x = 3 \): \( 192 \)

### Completed Table

Here is the completed table with the calculated and provided values:

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

**Note:** The values for Building 1 at \( x = 1 \) and \( x = 3 \) have been rounded to the nearest whole number.