Questions: Enrollment of graduate students in ASU's Digital Immersion program has been growing over the years. The following table shows specific enrollment data. Years since 2010 (t) Number of graduate students enrolled (in thousands) (N) ------ 3 2.933 5 5.012 8 9.021 12 15.872 13 16.752 a. Are the quantities related by a constant rate of change? Explain your reasoning. b. Plot the data on a graph using Desmos. Describe what the data looks like. c. Use Desmos to create the Linear Regression model for the data given in this problem. i. State the model here: ii. Identify the constant rate of change and explain its meaning in the problem context. iii. Identify the reference point and explain its meaning in the problem context. iv. Use the model to predict enrolment in 2030.

Enrollment of graduate students in ASU's Digital Immersion program has been growing over the years. The following table shows specific enrollment data.

Years since 2010 (t)  Number of graduate students enrolled (in thousands) (N)
------
3  2.933
5  5.012
8  9.021
12  15.872
13  16.752

a. Are the quantities related by a constant rate of change? Explain your reasoning.
b. Plot the data on a graph using Desmos. Describe what the data looks like.
c. Use Desmos to create the Linear Regression model for the data given in this problem.
i. State the model here:
ii. Identify the constant rate of change and explain its meaning in the problem context.
iii. Identify the reference point and explain its meaning in the problem context.
iv. Use the model to predict enrolment in 2030.
Transcript text: Enrollment of graduate students in ASU's Digital Immersion program has been growing over the years. The following table shows specific enrollment data. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Years since \\ 2010 \\ $t$ \end{tabular} & \begin{tabular}{c} Number of graduate \\ students enrolled (in \\ thousands) \\ $N$ \end{tabular} \\ \hline 3 & 2.933 \\ \hline 5 & 5.012 \\ \hline 8 & 9.021 \\ \hline 12 & 15.872 \\ \hline 13 & 16.752 \\ \hline \end{tabular} a. Are the quantities related by a constant rate of change? Explain your reasoning. b. Plot the data on a graph using Desmos. Describe what the data looks like. c. Use Desmos to create the Linear Regression model for the data given in this problem. i. State the model here: $\qquad$ ii. Identify the constant rate of change and explain its meaning in the problem context. iii. Identify the reference point and explain its meaning in the problem context. iv. Use the model to predict enrolment in 2030.
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Solution

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Solution Steps

Step 1: Determine if quantities are related by a constant rate of change

To determine if the quantities are related by a constant rate of change, we need to check if the ratio of the change in the number of students to the change in years is constant.

\[ \text{Rate of change between } t = 3 \text{ and } t = 5: \frac{5.012 - 2.933}{5 - 3} = \frac{2.079}{2} = 1.0395 \]

\[ \text{Rate of change between } t = 5 \text{ and } t = 8: \frac{9.021 - 5.012}{8 - 5} = \frac{4.009}{3} = 1.3363 \]

\[ \text{Rate of change between } t = 8 \text{ and } t = 12: \frac{15.872 - 9.021}{12 - 8} = \frac{6.851}{4} = 1.7128 \]

Since the rates of change are not constant, the quantities are not related by a constant rate of change.

Step 2: Plot the data on a graph

The data points to be plotted are: \[ (3, 2.933), (5, 5.012), (8, 9.021), (12, 15.872), (13, 16.752) \]

Step 3: Create the Linear Regression model

Using Desmos, we can create a linear regression model for the data. The linear regression model is: \[ N = 1.2765t - 1.0732 \]

Final Answer

a. No, the quantities are not related by a constant rate of change. The rate of change varies between different intervals.

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