Math 143 Week 7 Desmos Activity Worksheet
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Boise State University *
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Course
143
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by AgentCrownDove34
M143 Week 7 Worksheet Math 143 Week 7 Activity Worksheet Cubic Regression Directions: These activity questions are written to follow the Desmos activity for the week. Once you have completed the weekly activity you will be able to answer these questions. You can complete the questions on any document and then hand in the document on Canvas. 1.
If the leading coefficient of a cubic function is positive, what do you know about the graph of the cubic function? If the leading coefficient of a cubic function is positive, the graph of the cubic function will rise on both ends as x extends to positive and negative infinity. 2.
When making observations, collecting and using data, there are typically limitations as to how far data can be used to make predictions. Which math 143 topic below best describes limitations. Explain your selection. a)
Linear, quadratic, cubic equations b)
Maximum and Minimums c)
Domains and Ranges d)
x
-intercepts Domains and ranges tell us the valid input and output values for a function. Knowing these limits helps us understand where our data works well for making predictions. It's like knowing the boundaries of a game - you can only play within those lines. 3.
How many x-intercepts must a cubic function have? Explain. A cubic function can have up to three x-intercepts, but it may have fewer depending on its shape and behavior.
M143 Week 7 Worksheet 4.
Given the graph below, what is a possible equation for the graph? Explain your process. f(x)=x
3
-8x
2
+4. x
3 3 x-intercepts -8x
2
minimum +4 maximum 5.
Using the graph in #4, locate the maximum and minimum value(s), if they exist. Explain how you determine whether you have a maximum or minimum value. Highest and lowest points of the curves. 6.
Explain what it means for a relation to be a function. Sketch the graph of a relation that is a function. Give a set of ordered pairs that do NOT represent a function. A relation is a function if each input (x-value) only goes to one output (y-value). A function's graph is like a curve where each vertical line touches only once. Example of ordered pairs that do NOT represent a function: (1, 2), (2, 3), (1, 4), (3, 5)
M143 Week 7 Worksheet 7.
For the following set of data, Concentration of Species A Mole/L
Rate M/(L*sec)
0 Mole/L 16.5 M/(L*sec) .5 Mole/L 23.4 M/(L*sec) 1 Mole/L 68.0 M/(L*sec) 1.5 Mole/L 131.5 M/(L*sec) 2 Mole/L 195.0 M/(L*sec) 2.5 Mole/L 239.6 M/(L*sec) 3 Mole/L 246.5 M/(L*sec) a)
Plot the data on Desmos. Make sure to choose and justify a window. Sketch the plot below. b)
What is the domain in this situation? Explain. The domain consists of the concentrations of Species A ranging from 0 Mole/L to 3 Mole/L.
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M143 Week 7 Worksheet c)
What is the range in this situation? Explain. The range encompasses the corresponding rates of reaction, which range from 16.5 M/(Lsec) to 246.5 M/(Lsec). d)
Using Desmos, find the cubic regression equation that best models the data. Write your equation below.
M143 Week 7 Worksheet e)
Discuss why a cubic equation fits the data best. A cubic equation fits the data best because it can capture the curved relationship between the concentration of Species A and the rate of reaction. The data doesn't follow a straight line or a simple curve, so a cubic equation, with its flexibility, can better match the data points. It's like using a more flexible tool to get a closer fit to the real relationship between the variables. f)
Describe the intervals on the model where the graph is increasing and the intervals on the model where the graph is decreasing. To describe the intervals where the graph of the model is increasing and decreasing, we examine the behavior of the derivative of the cubic function. Increasing Intervals: The graph of the model is increasing where the derivative of the cubic function is positive. This means that as the concentration of Species A increases, the rate of reaction also increases. Decreasing Intervals: Conversely, the graph of the model is decreasing where the derivative of the cubic function is negative. This implies that as the concentration of Species A increases, the rate of reaction decreases. g)
Explain how you would find the rate when the concentration is 4.5 Mole/L. Find the rate when the concentration is 4.5 Mole/L. Using the regression equation we can plot the data set in Desmos and find the intersection. The rate when the concentration is 4.5 Mole/L is: -147.905