Of those using Brand A in any month, 70% continue to use it in the following month, 20% switch to Brand B, and 10% switch to Brand C. Of those using Brand B in any month, 80% continue to use it in the following month, 10% switch to Brand A, and 10% switch to Brand C. Of those using Brand C in any month, 70% continue to use it in the following month, 10% switch to Brand A, and 20% switch to Brand B. (a) What is the stochastic matrix P for this situation?

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

pretty sure it's false