A new flu virus is introduced when a stranger visits an isolated village of 8000 people. Every infected person infects two more each day. How do you write an exponential function to model the number of UNINFECTED people?
1 Answer
Explanation:
Let i(n) be the number of infected people and u(n) the number of uninfected people, both on the n-th day.
Let x(n) be the number of people who got infected on the n-th day. The relation between i(n) and x(n) is given by:
Let's assume the stranger leaves before the next day.
Taking the day the stranger arives as the 0-th day and assuming he infects two people on that day, then
The two people infected now will also infect two other people, meaning that:
Some more relations become clear:
As every person infects two people per day, then
This a recurrence relation for the number of infected people at a given day:
# i(2) = 3i(1)=18=3^2*2#
#i(3) = 3i(2)=54 = 3^3*2#
Analogously, we can figure out that
Hence the number of uninfected people on day n is