Question
Four points are plotted on a coordinate plane, and a line is graphed through them. The x-axis is labeled Days and ranges from 0 to 600 in increments of 20. The y-axis is labeled Weight in Pounds and ranges from 250 to 2,500 in increments of 250.
An elephant calf is born weighing 282 pounds and gains about 2.5 pounds each day for its first year of life. After one year, the calf weighs approximately 1,195 pounds. The graph represents the line of best fit for the data. Which of the following interpretations of the slope is accurate?
(1 point)
Responses
The calf gains 365 pounds in 913 days.
The calf gains 365 pounds in 913 days.
The calf gains 5 pounds every 2 days.
The calf gains 5 pounds every 2 days.
The calf gains 737 pounds over 182 days.
The calf gains 737 pounds over 182 days.
The calf gains an average of 1,195 pounds over one year of life.
An elephant calf is born weighing 282 pounds and gains about 2.5 pounds each day for its first year of life. After one year, the calf weighs approximately 1,195 pounds. The graph represents the line of best fit for the data. Which of the following interpretations of the slope is accurate?
(1 point)
Responses
The calf gains 365 pounds in 913 days.
The calf gains 365 pounds in 913 days.
The calf gains 5 pounds every 2 days.
The calf gains 5 pounds every 2 days.
The calf gains 737 pounds over 182 days.
The calf gains 737 pounds over 182 days.
The calf gains an average of 1,195 pounds over one year of life.
Answers
GPT-4o mini
To determine the accurate interpretation of the slope from the context provided, we should analyze the weight gain of the elephant calf.
The calf gains 2.5 pounds each day. Over the course of a year (365 days), this results in a total weight gain of:
\[ 2.5 \text{ pounds/day} \times 365 \text{ days} = 912.5 \text{ pounds} \]
The calf's weight at the start is 282 pounds, and after one year (365 days), it weighs approximately 1,195 pounds:
\[ 282 \text{ pounds} + 912.5 \text{ pounds} = 1,194.5 \text{ pounds} \approx 1,195 \text{ pounds} \]
Now, interpreting the slope in the context of the graph, where the x-axis represents days and the y-axis represents weight in pounds, the slope represents the rate of weight gain per day.
Since the calf gains 2.5 pounds every day, we can analyze the options given:
1. "The calf gains 365 pounds in 913 days." - **Incorrect**; the weight gain doesn't match the rate.
2. "The calf gains 5 pounds every 2 days." - **Correct**; since gaining 2.5 pounds per day means gaining 5 pounds over 2 days.
3. "The calf gains 737 pounds over 182 days." - **Incorrect**; does not accurately reflect the growth rate.
4. "The calf gains an average of 1,195 pounds over one year of life." - **Incorrect**; this is not a direct interpretation of the slope.
Thus, the correct response is:
**The calf gains 5 pounds every 2 days.**
The calf gains 2.5 pounds each day. Over the course of a year (365 days), this results in a total weight gain of:
\[ 2.5 \text{ pounds/day} \times 365 \text{ days} = 912.5 \text{ pounds} \]
The calf's weight at the start is 282 pounds, and after one year (365 days), it weighs approximately 1,195 pounds:
\[ 282 \text{ pounds} + 912.5 \text{ pounds} = 1,194.5 \text{ pounds} \approx 1,195 \text{ pounds} \]
Now, interpreting the slope in the context of the graph, where the x-axis represents days and the y-axis represents weight in pounds, the slope represents the rate of weight gain per day.
Since the calf gains 2.5 pounds every day, we can analyze the options given:
1. "The calf gains 365 pounds in 913 days." - **Incorrect**; the weight gain doesn't match the rate.
2. "The calf gains 5 pounds every 2 days." - **Correct**; since gaining 2.5 pounds per day means gaining 5 pounds over 2 days.
3. "The calf gains 737 pounds over 182 days." - **Incorrect**; does not accurately reflect the growth rate.
4. "The calf gains an average of 1,195 pounds over one year of life." - **Incorrect**; this is not a direct interpretation of the slope.
Thus, the correct response is:
**The calf gains 5 pounds every 2 days.**