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.

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: