Chapter 4.2, Problem 49E

(a)

To determine

To calculate: The proportion of accurate responses after $3$ trials when the proportion P of accurate responses in a learning theory subject after n trials is given by the function as $P=\frac{0.83}{\left(1+e^{-0.2n}\right)}$

(b)

To determine

To calculate: The proportion of accurate responses after $7$ trials when the proportion P of accurate responses in a learning theory subject after n trials is given by the function as,

$P=\frac{0.83}{\left(1+e^{-0.2n}\right)}$

(c)

To determine

To graph: The model by using technology which represents the proportion P of accurate responses in a learning theory subject after n trials is given as $P=\frac{0.83}{\left(1+e^{-0.2n}\right)}$ and also determine the number of trials required in order that the proportion of the accurate responses is $0.75$.

(d)

To determine

Whether the limit of proportion of accurate responses have some value or not as n increases without bound and give reason when the proportion P of accurate responses in a learning theory subject after n trials is given as $P=\frac{0.83}{\left(1+e^{-0.2n}\right)}$.