A school board has a plan to increase participation

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 69E
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A school board has a plan to increase participation in the
PTA. Currently only about 27 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 81 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.
(a) What is the carrying capacity K for a logistic
model of P versus m?
K =
(b) Find the constant b for a logistic model.
b =
(c) Find ther value for a logistic model. Round
your answer to three decimal places.
r =
(d) Find a logistic model for P versus m.
P =
Transcribed Image Text:A school board has a plan to increase participation in the PTA. Currently only about 27 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 81 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. (a) What is the carrying capacity K for a logistic model of P versus m? K = (b) Find the constant b for a logistic model. b = (c) Find ther value for a logistic model. Round your answer to three decimal places. r = (d) Find a logistic model for P versus m. P =
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