Please provide brief explanation or calculations A populatio

Please provide brief explanation or calculations.

A population grows according to an exponential growth model, with initial population P0 = 214 and common ratio r = 1.1 .

(a) Find P1 , P2 , P3 , and P4 .

(b) Find P20 .

Solution

Given P0 = 214, r=1.1.

For the exponential growth model, with common ratio r,

we have two formulas for the size Pn of the nth?generation:

Pn = rPn?1 and Pn = r^n?1P1.

so From Pn = rPn?1;

   a) P1=rPn-1

            =1.1(P1-1)

           =1.1(P0) =1.1(214)

           =235.4

       P2=1.1(P2-1)

            =1.1(P1)

            =1.1(235.4)           ( from above P1=235.4)

           =258.94

   P3=1.1(P3-1)

        =1.1(P2)

       =1.1(258.94)    ( from above P2=258.94)

      =284.834

P4=1.1(P4-1)

      =1.1(P3)

     =1.1(284.834)              (from above P3=284.834)

     = 313.317

b) From formula Pn = r^n?1P1.

               P20=(1.1)^(20-1)(235.4 )                    (from above P1=235.4)

                     =6.11(235.4)

                     =1439.68.