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


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Answer 1

To find the number of flu cases for each building at different days since the first reported case (x), we will evaluate the given function for Building 1 and take the values from the graph for Building 2.

### Building 1:
The function for Building 1 is given by:
\( f(x) = 14.25x^2 + 3 \)

We will calculate this function for x = 0, 1, 2, and 3.

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

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

### Building 2:
From the graph, we have the following data points:
- At x = 0, the value is 3
- At x = 1, the value is 12
- At x = 2, the value is 48
- At x = 3, the value is 192

### Summary Table:
Now, we can fill in the table:

| x | Building 1 | Building 2 |
|----|------------|------------|
| 0 | 3 | 3 |
| 1 | 17 | 12 |
| 2 | 60 | 48 |
| 3 | 131 | 192 |

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