Learning thoery in a learning theory project, the proportion p of correct responses after n trials can be modeled by p = 0.83/(1+e-02n).
(a) find the proportion of correct responses after 3 trials.
(b) find the proportion of correct responses after 7 trials.
(c) use a graphing utility to graph the model. find the number of trials required for the porportion of correct responses to be 0.75.
(d) does the porportion of correct responses have a limit as n increase without bound? explain your reasoning.

a)

b)

c)

And then if we solve for t we got:

d) If we find the limit when n tend to infinity for the function we have this:

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

Step-by-step explanation:

For this case we have the following expression for the proportion of correct responses after n trials:

Part a

For this case we just need to replace the value of n=3 in order to see what we got:

So the number of correct reponses  after 3 trials is approximately 0.536.

Part b

For this case we just need to replace the value of n=7 in order to see what we got:

So the number of correct responses after 7 weeks is approximately 0.666.

Part c

For this case we want to solve the following equation:

And we can rewrite this expression like this:

Now we can apply natural log on both sides and we got:

And then if we solve for t we got:

And we can see this on the plot attached.

Part d

If we find the limit when n tend to infinity for the function we have this:

So then the number of correct responses have a limit and is 0.83 as n increases without bound.

step-by-step explanation:

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step-by-step explanation:

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