Question
Which of the following functions best models the data represented by the scatterplot shown below?
A scatter plot shows x values from 0 to 18 and y values from 0 to 3000 with 10 data points showing a positive relationship. The points are at (7, 402), (13, 1362), and (11, 978).
A. y=25x+20
B. y=8x^2 + 10
C. y= 2^x + 12
D. y = 160x - 100
A scatter plot shows x values from 0 to 18 and y values from 0 to 3000 with 10 data points showing a positive relationship. The points are at (7, 402), (13, 1362), and (11, 978).
A. y=25x+20
B. y=8x^2 + 10
C. y= 2^x + 12
D. y = 160x - 100
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine which function best models the data represented by the scatterplot, we need to analyze the options given based on the observed positive relationship between the x and y values.
1. **Linear Model (Option A: y = 25x + 20)**: This is a linear function, which means it has a constant rate of change. Based on the data points, we need to check if this option aligns with them. For instance, plugging in x = 7 gives y = 25(7) + 20 = 175, which is significantly lower than the y value of 402 at that x value. So, this doesn't fit well.
2. **Quadratic Model (Option B: y = 8x^2 + 10)**: This is a quadratic function. Let's see if it makes sense for our points. x = 7 gives y = 8(7^2) + 10 = 8(49) + 10 = 392 + 10 = 402. This matches the point (7, 402). For x = 11, y = 8(11^2) + 10 = 8(121) + 10 = 968 + 10 = 978, which also matches. For x = 13, y = 8(13^2) + 10 = 8(169) + 10 = 1352 + 10 = 1362, which matches too. This function fits all three points perfectly and follows the trend.
3. **Exponential Model (Option C: y = 2^x + 12)**: This is an exponential function. For x = 7, y = 2^7 + 12 = 128 + 12 = 140, which is too low. For x = 11, y = 2^11 + 12 = 2048 + 12 = 2060, which is too high. This function does not fit well.
4. **Linear Model (Option D: y = 160x - 100)**: Testing this function, for x = 7: y = 160(7) - 100 = 1120 - 100 = 1020, which is too high. For x = 11: y = 160(11) - 100 = 1760 - 100 = 1660, which is again too high. This does not fit the data.
After evaluating the options, the quadratic function **y = 8x^2 + 10** (Option B) best models the data since it fits all given points perfectly and follows the positive trend of the scatterplot.
1. **Linear Model (Option A: y = 25x + 20)**: This is a linear function, which means it has a constant rate of change. Based on the data points, we need to check if this option aligns with them. For instance, plugging in x = 7 gives y = 25(7) + 20 = 175, which is significantly lower than the y value of 402 at that x value. So, this doesn't fit well.
2. **Quadratic Model (Option B: y = 8x^2 + 10)**: This is a quadratic function. Let's see if it makes sense for our points. x = 7 gives y = 8(7^2) + 10 = 8(49) + 10 = 392 + 10 = 402. This matches the point (7, 402). For x = 11, y = 8(11^2) + 10 = 8(121) + 10 = 968 + 10 = 978, which also matches. For x = 13, y = 8(13^2) + 10 = 8(169) + 10 = 1352 + 10 = 1362, which matches too. This function fits all three points perfectly and follows the trend.
3. **Exponential Model (Option C: y = 2^x + 12)**: This is an exponential function. For x = 7, y = 2^7 + 12 = 128 + 12 = 140, which is too low. For x = 11, y = 2^11 + 12 = 2048 + 12 = 2060, which is too high. This function does not fit well.
4. **Linear Model (Option D: y = 160x - 100)**: Testing this function, for x = 7: y = 160(7) - 100 = 1120 - 100 = 1020, which is too high. For x = 11: y = 160(11) - 100 = 1760 - 100 = 1660, which is again too high. This does not fit the data.
After evaluating the options, the quadratic function **y = 8x^2 + 10** (Option B) best models the data since it fits all given points perfectly and follows the positive trend of the scatterplot.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.