In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434. (a) Write an equation expressing the number y of shopping centers in terms of the number x of years after 1991. (b) When will the number of shopping centers reach 60,000? (a) The equation is y=x+ (Type integers or decimals.) (b) The number of shopping centers will reach 60,000 in the year (Round down to the nearest year.)
In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434. (a) Write an equation expressing the number y of shopping centers in terms of the number x of years after 1991. (b) When will the number of shopping centers reach 60,000? (a) The equation is y=x+ (Type integers or decimals.) (b) The number of shopping centers will reach 60,000 in the year (Round down to the nearest year.)
Chapter4: Linear Functions
Section4.3: Fitting Linear Models To Data
Problem 24SE: Table 6 shows the year and the number ofpeople unemployed in a particular city for several years....
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![### Analysis of Shopping Centers Growth Over Time
In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434.
**(a) Writing an Equation**
To express the number \( y \) of shopping centers in terms of the number \( x \) of years after 1991, we can use a linear equation.
\[ \text{The equation is } y = \] [ ][ ] \( x \) + [ ]
\[ \text{Type integers or decimals.} \]
**(b) Predicting Future Numbers**
To determine when the number of shopping centers will reach 60,000:
\[ \text{The number of shopping centers will reach 60,000 in the year } \] [ ][ ]
\[ \text{Round down to the nearest year.} \]
### Explanation of the Instructions
1. **Step (a) - Writing the Equation**:
- You will need to calculate the slope (rate of change) of the number of shopping centers per year between 1991 and 2001.
- Then, use the point-slope form to develop the linear equation that models this growth.
2. **Step (b) - When Number Will Reach 60,000**:
- Using the equation from step (a), solve for \( x \) when \( y = 60,000 \).
- Round down the resulting year to the nearest whole number.
This activity involves understanding linear relationships, specifically how to create and use a linear equation to project future values based on historical data.
### Visual Aids and Graphs (If Applicable)
- **Graph**: Display the number of shopping centers on the y-axis and the years on the x-axis, marking points for the year 1991 and 2001.
- **Slope Calculation**: Use a table to show the calculation of the increase in shopping centers per year.
Feel free to transpose these instructions and inputs onto your educational platform for a comprehensive learning module.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97184fab-fce4-43b1-85fd-c47064c00bbe%2Fc3ac280a-bf84-4796-8139-dd4db8166385%2Fxt2gji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Shopping Centers Growth Over Time
In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434.
**(a) Writing an Equation**
To express the number \( y \) of shopping centers in terms of the number \( x \) of years after 1991, we can use a linear equation.
\[ \text{The equation is } y = \] [ ][ ] \( x \) + [ ]
\[ \text{Type integers or decimals.} \]
**(b) Predicting Future Numbers**
To determine when the number of shopping centers will reach 60,000:
\[ \text{The number of shopping centers will reach 60,000 in the year } \] [ ][ ]
\[ \text{Round down to the nearest year.} \]
### Explanation of the Instructions
1. **Step (a) - Writing the Equation**:
- You will need to calculate the slope (rate of change) of the number of shopping centers per year between 1991 and 2001.
- Then, use the point-slope form to develop the linear equation that models this growth.
2. **Step (b) - When Number Will Reach 60,000**:
- Using the equation from step (a), solve for \( x \) when \( y = 60,000 \).
- Round down the resulting year to the nearest whole number.
This activity involves understanding linear relationships, specifically how to create and use a linear equation to project future values based on historical data.
### Visual Aids and Graphs (If Applicable)
- **Graph**: Display the number of shopping centers on the y-axis and the years on the x-axis, marking points for the year 1991 and 2001.
- **Slope Calculation**: Use a table to show the calculation of the increase in shopping centers per year.
Feel free to transpose these instructions and inputs onto your educational platform for a comprehensive learning module.
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