A school board has a plan to increase participation in the PTA. Currently only about 29 parents attend meetings. Suppose the school board plan results in logistic growth of attendance. The school board believes their plan can eventually lead to an attendance level of 87 parents. In the absence of limiting factors the school board believes its plan can increase participation by 10% each month. Let m denote the number of months since the participation plan was put in place, and let P be the number of parents attending PTA meetings.

Find a logistic model for P versus m.

Guest Nov 22, 2015

#1**0 **

This is much like a lot of the financial problems posted on this forum

m =number of months to reach 87

P= number of attendees now

We need to find the equation that defines how long it will take to get to 87 (The future value or Pf)

Pf = P ( 1 + i)^m = 87 i was given as 10 percent or 0.010 so Pf = P(1.010)^m = 87 and P was given as starting at 29

87 = 29 (1.010)^m

~jc

Guest Nov 22, 2015

#3**0 **

This is much like a lot of the financial problems posted on this forum

m =number of months to reach 87

P= number of attendees now

We need to find the equation that defines how long it will take to get to 87 (The future value or Pf)

Pf = P ( 1 + i)^m = 87 i was given as 10 percent or 0.010 so Pf = P(1.010)^m = 87 and P was given as starting at 29

87 = 29 (1.010)^m

Guest #2 is right...it is wrong, because I said 10 percent was .01....it is .1 D'oh!

should be P = 87 =29(1.1)^m Sorry ! It will take 11,5 months to reach 87 people using this model !

~ jc (almost nearly close to the possible answer about 75 % of the time! ha)

Guest Nov 22, 2015

#4**0 **

how is that the model?? Ik im supposed 2 plug it into the calc...BUT idk what to plug in...

Guest Nov 22, 2015

#5**0 **

Well the MODEL would be

Pf = P (1.10)^m Where P is the number of peole who attend NOW (29) Pf = the number of people you would like to see attend (the problem stated 87)

When you plug in those numbers and solve for 'm' , you will find out how many months it will take if you anticipate 10% growth per month (which is what the problem stated)

Say if you want to see 130 people attending that would be Pf 130 = 29(1.1)^m solving for 'm' shows it will take 15.7 months See?

~jc

Guest Nov 22, 2015

#6**+5 **

I think we need a logisitc growth model here......this is given by:

P = [ P_{0}K ] / [ P_{0} + (K - P_{0})e^(-rm) ]

Where P_{0} = 29 = the initial no. of people K = 87 = the max no. of people r = 10% = .1 and m is the number of months .....so we have

P = [29 * 87] / [ 29 + ( 87 - 29)e^(-.1m) ] = [2523] / [58e^(-.1m) + 29 ]

Here's the graph......notice that 87 is the "carrying capacity" ........https://www.desmos.com/calculator/bs1mlbrbrc

[ Also....the graph is only valid for m >= 0 ]

CPhill
Nov 22, 2015

#7**0 **

A little more than what I thought they might be looking for (obviously).....and outside my realm ! Hopefully that is what they needed...

Thanx Chris....

~jc

Guest Nov 22, 2015

#10**0 **

the model???

like it has to equal like this:

P =

this is the problem:

A school board has a plan to increase participation in the PTA. Currently only about 29 parents attend meetings. Suppose the school board plan results in logistic growth of attendance. The school board believes their plan can eventually lead to an attendance level of 87 parents. In the absence of limiting factors the school board believes its plan can increase participation by 10% each month. Let m denote the number of months since the participation plan was put in place, and let P be the number of parents attending PTA meetings.

What is the carrying capacity K for a logistic model of P versus m?

K=87

(b) Find the constant b for a logistic model.

b=2

(c) Find the r value for a logistic model. Round your answer to three decimal places.

r=.095

QUESTION:

(d) Find a logistic model for P versus m.

Guest Nov 22, 2015