Problema Solution
Let's assume that the pattern above is maintained; that is, each newly infected victim will themselves infect 7 other people. Then the function modeling the number of infected victims will be
N(x) = 7x, where x is the "generation" of contact.
In generation 0, the Chinese doctor becomes infected.
In generation 1, the doctor infects seven other people.
In generation 2, each of these seven victims in turn infects seven new victims.
etc.
Question: How many "generations" are required before at least 1 million people are infected? If we assume each generation lasts two days, how long will this take?
Answer provided by our tutors
N(x) = 7x, where x is the "generation" of contact
N(0) = 1
N(1) = 7*N(0) = 7*1
N(2) = 7*N(1) = 7*7*1 = 7^2
N(3) = = 7^3
we assume each generation lasts two days means we need to find x such that N(x) + N(x + 1) >= 1 million or:
7^x + 7^(x + 1) <= 10^6
7^x(1 + 7) <= 10^6
7^x <= (10^6)/8
x <= 6.03
click here to see the step by step solution of the inequality:
for x = 6 we have:
N(6) + N(7) = 7^6 + 7^7 = 941,192
for x = 7
N(7) + N(8) = 7^7 + 7^8 = 6,588,344
7 generations are required before at least 1 million people are infected.