Question

A town has a population of 4000 and grows at 3.5% every year. To the nearest year, how long will it be until the population will reach 7500?

Answer 1

18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.

Step-by-step explanation:

The given is,

             Population of 4000

             Rate of grow 3.5% every year

             Population after few years 7500

Step:1

            Formula to calculate the population with the grow rate every year,

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

           Where,

                    F - Population after t years

                   P - Initial population

                    r - Rate of grow

                    t - No.of years

          From given,

                  F = 7500

                  P = 4000

                   r = 3.5%

        Equation becomes (1),

                    $7500=4000(1+0.035)^{t}$

                     $\frac{7500}{4000} = (1+0.035)^{t}$

                   1.875 = $(1+0.035)^{t}$

                   $1.875 = (1.035)^{t}$

       Take log on both sides,

              $log 1.875 = (t)log 1.035$

       Substitute log values,

                 $0.2730= (t) 0.014940349$

                          $t = \frac{0.273}{0.014940349}$

                             = 18.273

                          t = 18.273 year

                             or

                         t = 18 years 3 months 2 weeks

Result:

          18.273 years will take to reach the population of 7500, if a town has a population of 4000 and grows at 3.5% every year.