Answer:
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.
