Question

Learning Theory In a group project in learning theory, a mathematical model for the proportion $P$ of correct responses after $n$ trials was found to be $$P=\frac{0.83}{1+e^{-0.2 n}}$$ (a) Find the limiting proportion of correct responses as $n$ approaches infinity. (b) Find the rates at which $P$ is changing after $n=3$ trials and $n=10$ trials.

          Learning Theory In a group project in learning theory, a mathematical model for the proportion $P$ of correct responses after $n$ trials was found to be
$$P=\frac{0.83}{1+e^{-0.2 n}}$$
(a) Find the limiting proportion of correct responses as $n$ approaches infinity.
(b) Find the rates at which $P$ is changing after $n=3$ trials and $n=10$ trials.

Added by Judy T.

Calculus: Early Transcendentals

James Stewart 8th Edition

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06/22/2023

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Learning Theory In a group project in learning theory, a mathematical model for the proportion $P$ of correct responses after $n$ trials was found to be $$P=\frac{0.83}{1+e^{-0.2 n}}$$ (a) Find the limiting proportion of correct responses as $n$ approaches infinity. (b) Find the rates at which $P$ is changing after $n=3$ trials and $n=10$ trials.