bilogy a new flu virus is introdused when a stranger visits an isilated vilige of 8000 people. Every infected person infect 2 more each day. write the exponential function to model the number of uninfected people.

Answer: u (n) = 8000-3n⋅2

Step-by-step 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:

i (n) = i (n-1) + x (n)

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

i (0) = x (0) = 2

u (0) = 8000-2=7998

The two people infected now will also infect two other people, meaning that:

x (1) = 2i (0) = 4

i (1) = i (0) + x (1) = 6

u (1) = 7998-x (1) = 7994=8000-i (1)

Some more relations become clear:

u (n) = u (n-1) - x (n)

u (n) = 8000-i (n)

As every person infects two people per day, then

x (n) = 2i (n-1)

Therefore

i (n) = i (n-1) + 2i (n-1) = 3i (n-1)

This a recurrence relation for the number of infected people at a given day:

i (n) = {3i (n-1)

if n is not equal to 2

if n=0

Implies

i (1) = 3i (0) = 6=31⋅2

i (2) = 3i (1) = 18=32⋅2

i (3) = 3i (2) = 54=33⋅2

Analogously, we can figure out that

i (n) = 3n⋅2

Hence the number of uninfected people on day n is

u (n) = 8000-3n⋅2