MA091-Written_Homework_5_Polynomials (1)
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School
University of Wisconsin, Whitewater *
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Course
141
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
3
Uploaded by GeneralWaterOkapi30
Name: Theresa Spicer
•
The Cumulative global capacity of wind power installations (C) , in gigawatts (GW) can be estimated by the polynomial where t is the number of years after the year 2000. •
Use an online tool such as desmos
, to graph this function and use your snipping tool to copy and past a picture of your function below.
•
In what year was the cumulative global capacity of wind power installations approximately 263GW?
2t^2-4t+23=263
Year 2011
263-23=240
2t^2-4t-240=0
t
≈
11 or t
≈
12
•
What is one other piece of information that you can interpret from the graph that you created?
You can see the increase in global wind power, the chart above shows rapid increase.
•
What is one other piece of information that you cannot interpret from the graph that you created?
You do not see what specific factors are influencing the growth of wind power. •
Valley Community College is presenting a series of plays. The profit, P, in dollars can be modeled by the equation , where x is the number of days.
•
Use an online tool, such as desmos
, to graph this function and use your snipping tool
and paste a picture of your function below.
•
When the graph crosses the x axis, what is indicated?
It shows the number of days the play earns no profit or loss.
•
Estimate approximately which day gives a maximum profit?
The approximated day that gives the maximum profit is the 225th day. •
Can you think of reasons on why the profit would peak and then decline again? It could peak as the publics intrest peaks, and then as they lose intreste again it will decline again.
•
Total Profit, P, is the difference between total revenue R and total cost C. Given the following functions for Revenue and Cost, determine the Profit equation, graph the equation, and answer the following related questions. In these equations we will assume that x represents the number
of parts produced at a manufacturing facility. Hint- the value is pretty large so scroll up on the y axis. Revenue: r(x)=1000x-x^2
Cost: c(x)=3400+10x
•
Determine what the equation for Profit, P is here.
profit=revenue-cost
p(x)=r(x)-c(x)
p(x)=(1000x-x^2)-(3400+10x)
=-x^2+990x-3400
•
Use an online tool, such as desmos
to graph this function and use your snipping tool and paste the picture of your function below
•
Can you think of what x could be in these equations other than the number of produced parts? It could be parts sold
•
What does the peak of your graph represent here?
Profit
•
What does it mean when your graph crosses the x axis?
It means that y is zero
•
Why might this graph peak and then decline, even though the number of parts is increasing?
The cost of making parts may be higher, so the overall revenue will be lower. •
What is one more piece of information that you can interpret from this graph?
You can see that demand for these parts are high, as they would not produce them if they were not selling.
•
What is one piece of information that you cannot interpret from this graph?
The demand for the current product. You have now way of knowing how many of each item will sell.
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