Question

mathematical thinking and reasoning
actively participate in effortful learning both individually and collectively
mathematicians who participate in effortful learning both individually and with others analyze problems in a way that make sense given the task.
work with a partner. the table shows the amount of nuclear electricity generated for consumer use in the united states over time. write a problem that can be solved using the given information. then exchange problems with another pair of students.

1. explain the problem.

a. what information is given?
b. what is being asked?

1. make a plan for how to solve the problem. describe any problem - solving strategies that you will use.
2. use your plan to solve the problem. then show that your solution is reasonable.

years since 1980 electricity generated by nuclear power (millions of kilowatt hours) percent of all electricity generated by nuclear power
0 251,116 11
5 383,691 15.5
10 576,862 19
15 673,402 20.1
20 753,893 19.8
25 781,986 19.3
30 806,968 19.6
35 797,178 19.6

Explanation:

1.

• a. Given information:
• The table shows two - sets of data. One is the number of years since 1980 (0, 5, 10, 15, 20, 25, 30, 35). The other is the amount of electricity generated by nuclear power in the United States in millions of kilowatt - hours (251,116; 383,691; 576,862; 673,402; 753,893; 781,986; 806,968; 797,178) and the percent of all electricity generated by nuclear power (11%; 15.5%; 19%; 20.1%; 19.8%; 19.3%; 19.6%; 19.6%).
• b. What is being asked: First, write a problem using the given information. Then exchange problems with another pair of students. After that, explain the problem (what is given and what is asked), make a plan to solve it, use the plan to solve it, and show that the solution is reasonable.

1. Plan:

• Problem - writing idea: We could ask to find the average rate of change of the electricity generated by nuclear power over a certain time period or predict the amount of nuclear - generated electricity in a future year using a linear or non - linear model (such as linear regression if it appears to be approximately linear). For example, find the average rate of change of the amount of electricity generated by nuclear power from year 0 to year 15.
• Solution strategy: To find the average rate of change, use the formula $\text{Average Rate of Change}=\frac{\Delta y}{\Delta x}$, where $y$ is the amount of electricity generated and $x$ is the number of years since 1980.

1. Solution:

• Let's find the average rate of change of the amount of electricity generated by nuclear power from year 0 to year 15.
• # Explanation:

Step 1: Identify the values of $y_1$, $y_2$, $x_1$, and $x_2$

When $x_1 = 0$, $y_1=251116$; when $x_2 = 15$, $y_2 = 753893$.

Step 2: Calculate the average rate of change

$\text{Average Rate of Change}=\frac{y_2 - y_1}{x_2 - x_1}=\frac{753893 - 251116}{15-0}=\frac{502777}{15}\approx33518.47$ (millions of kilowatt - hours per year).

• Reasonableness check: The value is positive, which makes sense since the amount of electricity generated by nuclear power generally increased from year 0 to year 15. Also, looking at the data points, the increase over 15 years divided by 15 gives a value that is in line with the general trend of growth shown in the table.

Answer:

The average rate of change of the amount of electricity generated by nuclear power from year 0 to year 15 is approximately 33518.47 million kilowatt - hours per year.