Comprehension
The following questions refer to the ”Ethan Hunt” scenario, which provides information across multiple tabs: a bar chart of Vulnerability Indices, a map of Day 1 Cases, a propagation model formula, and a table of city vulnerabilities (instability, hospital capacity, etc.).
Part B: For each of the following statements, select Yes if the statement accurately
reflects the information given in the tabs. Otherwise, select No.
Question: 1
The city with the highest vulnerability index saw less than 30 new cases on Day 2.
The city with the highest vulnerability index saw less than 30 new cases on Day 2.
Show Hint
When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.
Updated On: Sep 30, 2025
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Solution and Explanation
Step 1: Identify the city with the highest VI. This is Athens with VI = 8.
Step 2: Find the Day 1 cases for Athens from the map: Cases\(_{D1}\) = 36.
Step 3: Use the formula to calculate total cases on Day 2. Cases\(_{t+1}\) = Cases\(_t\) \(\times\) (1 + VI/10). Cases\(_{D2}\) = floor(36 \(\times\) (1 + 8/10)) = floor(36 \(\times\) 1.8) = floor(64.8) = 64.
Step 4: Calculate the number of new cases on Day 2. New Cases = Cases\(_{D2}\) - Cases\(_{D1}\) = 64 - 36 = 28.
Step 5: Evaluate the statement. 28 is less than 30. The statement is true.
Step 2: Find the Day 1 cases for Athens from the map: Cases\(_{D1}\) = 36.
Step 3: Use the formula to calculate total cases on Day 2. Cases\(_{t+1}\) = Cases\(_t\) \(\times\) (1 + VI/10). Cases\(_{D2}\) = floor(36 \(\times\) (1 + 8/10)) = floor(36 \(\times\) 1.8) = floor(64.8) = 64.
Step 4: Calculate the number of new cases on Day 2. New Cases = Cases\(_{D2}\) - Cases\(_{D1}\) = 64 - 36 = 28.
Step 5: Evaluate the statement. 28 is less than 30. The statement is true.
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Question: 2
In the city with the lowest hospital surge capacity, the number of new cases on Day 3 was greater than the number of daily beds.
In the city with the lowest hospital surge capacity, the number of new cases on Day 3 was greater than the number of daily beds.
Show Hint
When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.
Updated On: Sep 30, 2025
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Solution and Explanation
Step 1: Identify the city with the lowest hospital surge capacity. This is Cagliari with 40 daily beds.
Step 2: Get the data for Cagliari: VI = 6, Cases\(_{D1}\) = 40.
Step 3: Calculate cases for Day 2 and Day 3. Cases\(_{D2}\) = floor(40 \(\times\) (1 + 6/10)) = floor(40 \(\times\) 1.6) = 64.
Cases\(_{D3}\) = floor(64 \(\times\) 1.6) = floor(102.4) = 102.
Step 4: Calculate new cases on Day 3. New Cases = Cases\(_{D3}\) - Cases\(_{D2}\) = 102 - 64 = 38.
Step 5: Evaluate the statement. New cases (38) are not greater than daily beds (40). The statement is false.
Step 2: Get the data for Cagliari: VI = 6, Cases\(_{D1}\) = 40.
Step 3: Calculate cases for Day 2 and Day 3. Cases\(_{D2}\) = floor(40 \(\times\) (1 + 6/10)) = floor(40 \(\times\) 1.6) = 64.
Cases\(_{D3}\) = floor(64 \(\times\) 1.6) = floor(102.4) = 102.
Step 4: Calculate new cases on Day 3. New Cases = Cases\(_{D3}\) - Cases\(_{D2}\) = 102 - 64 = 38.
Step 5: Evaluate the statement. New cases (38) are not greater than daily beds (40). The statement is false.
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Question: 3
Cities with a vulnerability index less than 5 have fewer than 10 new cases on Day 2.
Cities with a vulnerability index less than 5 have fewer than 10 new cases on Day 2.
Show Hint
When analyzing exponential growth over multiple periods, the growth rate (multiplier) is typically more influential on the final outcome than the initial starting value. A city with a significantly higher rate will likely overtake a city with a higher starting value but a lower rate.
Updated On: Sep 30, 2025
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Solution and Explanation
Step 1: Identify cities with VI<5. These are London (VI=4.5) and Prague (VI=4.5).
Step 2: Check the condition for London. Cases\(_{D1}\) = 23. Cases\(_{D2}\) = floor(23 \(\times\) (1 + 4.5/10)) = floor(23 \(\times\) 1.45) = floor(33.35) = 33.
New cases = 33 - 23 = 10. The number of new cases (10) is not "fewer than 10".
Step 3: Since we have found a counterexample, the statement is false. (Prague's new cases are 12, which also fails the condition).
Step 2: Check the condition for London. Cases\(_{D1}\) = 23. Cases\(_{D2}\) = floor(23 \(\times\) (1 + 4.5/10)) = floor(23 \(\times\) 1.45) = floor(33.35) = 33.
New cases = 33 - 23 = 10. The number of new cases (10) is not "fewer than 10".
Step 3: Since we have found a counterexample, the statement is false. (Prague's new cases are 12, which also fails the condition).
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