Question

The population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.

Answer 1

After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.

Step-by-step explanation:

The given is,

           Population of Boomtown is 475,000

           Increasing at a rate of 3.75% each year    

           After few years population exceed 1 million people

Step:1

          Formula to calculate population with a given rate of increase,

                                       $F =P(1+r)^{t}$..............................(1)

         Where,

                   F - Population after t years

                   P - Population at initial

                    r - Rate of increase

                    t - No.of years

        From the given values,

                      F = 1000000

                      P = 475,000

                       r = 3.75%

          Equation (1) becomes,

                        $1000000 =475000(1+ 0.0375)^{t}$

                          $\frac{1000000}{475000} = (1.0375)^{t}$

                     $2.1052632=(1.0375)^{t}$

        Take log on both sides,

                 $log 2.1052632 =(t) log 1.0375$

       Substitute log values,

                     $0.3233064= (t) 0.015988$

                                   $t = \frac{0.3233064}{0.015988}$

                                      = 20.2216

                                   t ≅ 20.222 years

Result:

        After 20.22 years the population exceed 1 million people, if the population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year.