Answer:
5380839 infected
Step-by-step 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
