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
𝑓
(
𝑥
)
=
14.25
𝑥
2
+
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 3
Building 2


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Answer 1

To fill in the table with the number of flu cases for each building based on the provided functions and graph points, we can calculate the cases for Building 1 using the given function and use the provided points for Building 2.

1. Building 1: We can use the function \( f(x) = 14.25x^2 + 3 \) to calculate the number of flu cases.

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

2. Building 2: From the graph points given, we can directly use the values:

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

Now, let's summarize the results in the table:

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

Thus, the completed table is:

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