Let f(t) be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is f(t) 0.027t2 + 0.216t + 53.296. %3D Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well? O The function is not a good model for the data O The function is a good model for the data. Estimate at what capacity U. S. nuclear power plants were working in 2010. % Round to the nearest whole percent. Predict when U. S. nuclear power plants will be working at full (100%) capacity. Enter the year this occurs.
Let f(t) be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is f(t) 0.027t2 + 0.216t + 53.296. %3D Use a graphing calculator to draw the graph of the model and, in the same viewing window, the scattergram of the data. Does the model fit the data well? O The function is not a good model for the data O The function is a good model for the data. Estimate at what capacity U. S. nuclear power plants were working in 2010. % Round to the nearest whole percent. Predict when U. S. nuclear power plants will be working at full (100%) capacity. Enter the year this occurs.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**U.S. Nuclear Power Plant Capacity Over Time**
The table below represents the capacities, in percentage, at which U.S. nuclear power plants have been operating over various years:
| Year | Percent |
|------|---------|
| 1975 | 56 |
| 1980 | 59 |
| 1985 | 58 |
| 1990 | 70 |
| 1995 | 76 |
| 2000 | 88 |
| 2004 | 89 |
**Mathematical Model**
Let \( f(t) \) be the capacity (in percent) at which U.S. nuclear power plants are working at \( t \) years since 1970. A model of the situation is given by:
\[ f(t) = 0.027t^2 + 0.216t + 53.296 \]
**Exercise: Data Visualization and Model Evaluation**
Using a graphing calculator:
1. Plot the graph of the function \( f(t) \).
2. Plot the scattergram using the data points from the table.
3. Evaluate: Does the model fit the data well?
- \( \circ \) The function is not a good model for the data.
- \( \circ \) The function is a good model for the data.
**Prediction Task**
Estimate at what capacity U.S. nuclear power plants were operating in 2010.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05d3adb9-7fe4-4d5a-99c8-26255e44b92b%2F037e4098-85d0-4f6a-856a-8994ee4119a7%2Fca255qs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**U.S. Nuclear Power Plant Capacity Over Time**
The table below represents the capacities, in percentage, at which U.S. nuclear power plants have been operating over various years:
| Year | Percent |
|------|---------|
| 1975 | 56 |
| 1980 | 59 |
| 1985 | 58 |
| 1990 | 70 |
| 1995 | 76 |
| 2000 | 88 |
| 2004 | 89 |
**Mathematical Model**
Let \( f(t) \) be the capacity (in percent) at which U.S. nuclear power plants are working at \( t \) years since 1970. A model of the situation is given by:
\[ f(t) = 0.027t^2 + 0.216t + 53.296 \]
**Exercise: Data Visualization and Model Evaluation**
Using a graphing calculator:
1. Plot the graph of the function \( f(t) \).
2. Plot the scattergram using the data points from the table.
3. Evaluate: Does the model fit the data well?
- \( \circ \) The function is not a good model for the data.
- \( \circ \) The function is a good model for the data.
**Prediction Task**
Estimate at what capacity U.S. nuclear power plants were operating in 2010.
![### Capacity of U.S. Nuclear Power Plants Over Time
The table below shows the percentage capacity at which U.S. nuclear power plants have been operating at various years since 1970:
| Year | Capacity (%) |
|------|--------------|
| 1990 | 70 |
| 1995 | 76 |
| 2000 | 88 |
| 2004 | 89 |
#### Mathematical Model
Let \( f(t) \) represent the capacity (in percent) of U.S. nuclear power plants operating at \( t \) years since 1970. The model representing this situation is given by:
\[ f(t) = 0.027t^2 + 0.216t + 53.296 \]
#### Graphing and Analysis
- Use a graphing calculator to plot the function \( f(t) \) and compare it with the scatter plot of the data provided in the table.
- Evaluate the fit of the model to the data.
**Options:**
- The function is not a good model for the data.
- The function is a good model for the data.
#### Estimations and Predictions
1. **Estimate the Capacity for 2010:**
- Calculate the capacity percentage for the year 2010 using the model. Round your answer to the nearest whole percent.
2. **Predict Full Capacity:**
- Determine the year when U.S. nuclear power plants will operate at full (100%) capacity using the model.
This exercise aids in understanding how mathematical modeling and calculations are used to predict trends and capacities in real-world scenarios like nuclear power plant operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05d3adb9-7fe4-4d5a-99c8-26255e44b92b%2F037e4098-85d0-4f6a-856a-8994ee4119a7%2Fzfdss8f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Capacity of U.S. Nuclear Power Plants Over Time
The table below shows the percentage capacity at which U.S. nuclear power plants have been operating at various years since 1970:
| Year | Capacity (%) |
|------|--------------|
| 1990 | 70 |
| 1995 | 76 |
| 2000 | 88 |
| 2004 | 89 |
#### Mathematical Model
Let \( f(t) \) represent the capacity (in percent) of U.S. nuclear power plants operating at \( t \) years since 1970. The model representing this situation is given by:
\[ f(t) = 0.027t^2 + 0.216t + 53.296 \]
#### Graphing and Analysis
- Use a graphing calculator to plot the function \( f(t) \) and compare it with the scatter plot of the data provided in the table.
- Evaluate the fit of the model to the data.
**Options:**
- The function is not a good model for the data.
- The function is a good model for the data.
#### Estimations and Predictions
1. **Estimate the Capacity for 2010:**
- Calculate the capacity percentage for the year 2010 using the model. Round your answer to the nearest whole percent.
2. **Predict Full Capacity:**
- Determine the year when U.S. nuclear power plants will operate at full (100%) capacity using the model.
This exercise aids in understanding how mathematical modeling and calculations are used to predict trends and capacities in real-world scenarios like nuclear power plant operations.
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