Question

18 months ago, the membership of a business marketer's professional organization was 3000. Today it is 4200. The number of members increases at a rate that is proportional to the current size of the membership and the difference between the total number of potential members and the current membership. If there are 30000 potential members, find a function that gives the number of members, and find the number of members 3 months from now. Round values in your function to 5 decimal places and round your answer to the 2nd part to the nearest member. P(t) Preview 3 months from now, there will be members.

Answer 1

18 months ago, the membership of a business marketer's professional organization was 3000. Today it is 4200. The number of members increases at a rate that is proportional to the current size of the membership and the difference between the total number of potential members and the current membership. If there are 30000 potential members, find a function that gives the number of members, and find the number of members 3 months from now. Round values in your function to 5 decimal places and round your answer to the 2nd part to the nearest member P(t) = 3 months from now, there will be members. CE) be the numbee members t mondho after be tHhe tohl umber ofpatenhal manbévs thu ne are Rreu nih dplt o Po > 1-0 cunrent time (mro) menbens Pa /No- Po / dt dt whene kis cnatant f foroprtsmalidy. Fer to, Pt) = P (ktNo P/ +1 P (t) Given ft-/8 , P(-18) = 3000 ( itk18)30,o - 41) ) = 4 2 0 (1-19 K (25,00D) = 42u0 - 18 (s8) K 4 2-/7 .', K = 63(258 (1+s) Hence P lt) = 4200 (1+ 63 (2580 =4250 Plt)= 420t t/63) 3/63 42uD 42uo 22 44 oD 21