Abiologist doing an experiment has a bacteria population cultured in a petri dish. after measuring, she finds that there are 11 million bacteria infected with the zeta-virus and 5.2 million infection-free bacteria. her theory predicts that 50% of infected bacteria will remain infected over the next hour, while the remaining of the infected manage to fight off the virus in that hour. similarly, she predicts that 80% of the healthy bacteria will remain healthy over the hour while the remaining of the healthy will succumb to the affliction modeling this as a markov chain, use her theory to predict the population of non-infected bacteria after 3 hour(s).

11.4 million

Step-by-step explanation:

Let's define the variables i and i' to represent the number of infected bacteria initially and after 1 hour, and the variables n and n' to represent the number of non-infected bacteria initially and after 1 hour. The biologist's theory predicts ...

0.50i +0.20n = i'

0.50i +0.80n = n'

In matrix form, the equation looks like ...

If i''' and n''' indicate the numbers after 3 hours, then (in millions), the numbers are ...

Carrying out the math, we find i''' = 4.8006 (million) and n''' = 11.3994 (million).

The population of non-infected bacteria is expected to be about 11.4 million after 3 hours.

25

step-by-step explanation: