Thank you for visiting A construction manager is monitoring the progress of building a new house The scatterplot and table show the percentage of the house still left to. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find which function best models the data for the percentage of the house left to build over time, we need to determine a linear model using the given data:
The data points are:
- (0, 100)
- (1, 86)
- (2, 65)
- (3, 59)
- (4, 41)
- (5, 34)
A linear relationship can be represented by the equation of a line: [tex]\( f(x) = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
### Step-by-step Breakdown:
1. Identify the Slope (m):
The slope [tex]\( m \)[/tex] tells us how much the percentage of the house left to build decreases each month.
We have the result: [tex]\( m \approx -13.457 \)[/tex]
2. Identify the Y-intercept (c):
The y-intercept [tex]\( c \)[/tex] is the percentage of the house left to build at the start (when [tex]\( x = 0 \)[/tex]).
We have the result: [tex]\( c \approx 97.81 \)[/tex]
3. Match with Given Options:
Now, compare these results to the options given:
- A) [tex]\( f(x) = -13.5x + 97.8 \)[/tex]
- B) [tex]\( f(x) = -13.5x + 7.3 \)[/tex]
- C) [tex]\( f(x) = 97.8x - 13.5 \)[/tex]
- D) [tex]\( f(x) = 7.3x - 97.8 \)[/tex]
The closest match based on both the slope and the y-intercept is option A, [tex]\( f(x) = -13.5x + 97.8 \)[/tex].
Therefore, the best function to model the data is option A: [tex]\( f(x) = -13.5x + 97.8 \)[/tex].
The data points are:
- (0, 100)
- (1, 86)
- (2, 65)
- (3, 59)
- (4, 41)
- (5, 34)
A linear relationship can be represented by the equation of a line: [tex]\( f(x) = mx + c \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the y-intercept.
### Step-by-step Breakdown:
1. Identify the Slope (m):
The slope [tex]\( m \)[/tex] tells us how much the percentage of the house left to build decreases each month.
We have the result: [tex]\( m \approx -13.457 \)[/tex]
2. Identify the Y-intercept (c):
The y-intercept [tex]\( c \)[/tex] is the percentage of the house left to build at the start (when [tex]\( x = 0 \)[/tex]).
We have the result: [tex]\( c \approx 97.81 \)[/tex]
3. Match with Given Options:
Now, compare these results to the options given:
- A) [tex]\( f(x) = -13.5x + 97.8 \)[/tex]
- B) [tex]\( f(x) = -13.5x + 7.3 \)[/tex]
- C) [tex]\( f(x) = 97.8x - 13.5 \)[/tex]
- D) [tex]\( f(x) = 7.3x - 97.8 \)[/tex]
The closest match based on both the slope and the y-intercept is option A, [tex]\( f(x) = -13.5x + 97.8 \)[/tex].
Therefore, the best function to model the data is option A: [tex]\( f(x) = -13.5x + 97.8 \)[/tex].
Thank you for reading the article A construction manager is monitoring the progress of building a new house The scatterplot and table show the percentage of the house still left to. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
