The population (in thousands) for alpha city, t years after january 1,2004 is modeled by the quadratic function p(t)=0.3t^2+6t+80. in what month of what year does alpha city’s population reach twice it’s initial population?

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.

the first one, all those points on the line just make a strait line.