Question

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?

Answer 1

Answer: At 24 February, 2014 the population gets twice of its initial population.

Step-by-step explanation:

Since we have given that

The population for Alpha City, t years after January 1, 2004 is given as

`P(t)=0.3t^2+6t+80`

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

So, our quadratic equation becomes,

`P(0)=0+0+80=80`

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

`P(t)=2* 80=160`

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

`160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{Using quadratic formula ,we get }\\\\t_(1,\:2)=(-60\pm √(60^2-4\cdot \:3\cdot \:800))/(2\cdot \:3)\\\\t=-29.14\ and\ t=9.149`

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.