Question

A population of 280 flying squirrels in a town in Honduras is growing at a rate of 9% every 6 months. How many squirrels will the be in 3 years? Round to the nearest whole number.

Answer 1

The 470 squirrels will be in 3 years, if a population of 280 flying squirrels in a town in Honduras is growing at a rate of 9% every 6 months.

Step-by-step explanation:

The given is,

                  280 flying squirrels

                  Growing at a rate of 9% every 6 months

Step:1

                 Formula to calculate the squirrels,

                                      $y = A (1+r)^{t}$...........................(1)

                 where, A = Initial count

                               r = Growing rate

                               t = Time

                  From the given,

                      A = 280 squirrels

                       r = 9 % = 0.09

                       t = 6        ( Growing rate is given for 6 months, for 3 years 36 months available, so t =$\frac{36}{6}$ = 6)

                 From equation (1),

                               $y =280(1+0.09)^{6}$

                                  $= 280 (1.09)^{6}$

                                  = (280)(1.6771)

                                  = 469.588

             Squirrels after 3 years, y ≅ 470 squirrels

                                 ( or )

Step:1

            Year will be converted to months,

                       3 years = 36 months

           For 6 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (280 × 0.09)+280 = 305.2 squirrels

           For 12 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (305.2 × 0.09)+305.2 = 332.668 squirrels

             For 18 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (332.668 × 0.09)+332.668 = 362.608 squirrels

           For 24 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (362.608 × 0.09)+362.608 = 395.243 squirrels

            For 30 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (395.243 × 0.09)+395.243 = 430.815 squirrels

             For 36 months,

                                     $=( Squirrels count )( Rate of grow ) +Squirrels count$

                                      = (430.815 × 0.09)+430.815 = 469.588 squirrels

               Squirrels after 3 years, y ≅ 470 squirrels

Result:

           The 470 squirrels will be in 3 years, if a population of 280 flying squirrels in a town in Honduras is growing at a rate of 9% every 6 months.