Question

B.Imagine you are 1 of the people who left the luncheon with a contagious disease and interacted with an average of 9 different people each day. How many people could potentially be infected in 7 days

Answer 1

5380839 infected

Explanation:

Let's do the calculations day by day, we have:

Day 1

That person spread 9 people.

Day 2

Each of the nine people infect 9 others, plus that person infected 9 others, therefore it would be:

9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = (9 x 9) + 9 = 9 ^ 2 + 9 (assume this number as first term + second term)

Day 3

By the end of day 2, there were a total of 9 ^ 2 persons (first term) will infect 9 each, which makes this figure:

9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 + 9 ^ 2 = 9x9 ^ 2 = 9 ^ 2. The second term will now become 9 ^ 2, plus another 9 infected by the person who started it all. Therefore it would remain:

9 ^ 3 + 9 ^ 2 + 9

Following the sequence would be:

Day 4

9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9

Day 5

9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9

Day 6

9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9

Day 7

9 ^ 7 + 9 ^ 6 + 9 ^ 5 + 9 ^ 4 + 9 ^ 3 + 9 ^ 2 + 9 = 5380839

Which means that in total there would be 5380839 infected