Learning theory in a typing class, the averege number n of words per minutes typed after t weeks of lessons can be modeled by n = 95/(1+8.5e- 0.12t).
(a) find the averege number of words per minute typed after 10 weeks.
(b) find the averege number of words per minute typed after 20 weeks.
(c) use a graphing utility to graph the model. find the number of weeks required to achieve an averege of 70 words per minute.
(d) does the number of words per minute have a limit at t increases without bound? explain your reasoning.

a)

b)

c)

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

So then the number of words per minute have a limit and is 95 as t increases without bound.

Step-by-step explanation:

For this case we have the following expression for the average number of words per minutes typed adter t weeks:

Part a

For this case we just need to replace the value of t=10 in order to see what we got:

So the number of words per minute typed after 10 weeks are approximately 27.

Part b

For this case we just need to replace the value of t=20 in order to see what we got:

So the number of words per minute typed after 20 weeks are approximately 54.

Part c

For this case we want to solve the following equation:

And we can rewrite this expression like this:

Now we can divide both sides by 8.5 and we got:

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 1 attached.

Part d

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

So then the number of words per minute have a limit and is 95 as t increases without bound.

show us the picture

step-by-step explanation:

show the !