An elephant calf weighs 282 at birth and gains about 2.5 pounds each day for the first year of its life. After a year the calf weighs approximately 1,195 pounds The graph represents the best fit for the data. Which of the following interpretations of the slope is accurate

Question

T
It gains 5 pounds every 2 days
Gains 737 pounds over 182 days
Gains an average of 1,185 pounds over the one year of life
It gains 365 pounds in 913 days
Points are (0,282), (182,737), (365,1195), (574,1650)

Answer 1

To determine the accurate interpretation of the slope, let's start by analyzing the information provided:

1. The elephant calf starts at a weight of 282 pounds at birth (point (0, 282)).
2. The calf gains approximately 2.5 pounds per day for the first year (365 days).
3. At the end of one year, the calf weighs around 1,195 pounds (point (365, 1195)).
4. The slope of the line on the graph represents the weight gain per time unit (in this case, days).

Let's calculate the total weight gain after one year:

• Weight gain per day = 2.5 pounds
• Total weight gain in one year (365 days) = 365 days × 2.5 pounds/day = 912.5 pounds
• Therefore, the weight at one year = 282 pounds + 912.5 pounds = 1194.5 pounds, which is consistent with the provided weight.

Now, let's check the options:

1. It gains 5 pounds every 2 days.

   • If it gains 2.5 pounds per day, then in 2 days it would gain 2.5 * 2 = 5 pounds. This statement is accurate.

2. Gains 737 pounds over 182 days.

   • In 182 days, it would gain 182 days * 2.5 pounds/day = 455 pounds (not 737). This statement is inaccurate.

3. Gains an average of 1,185 pounds over the one year of life.

   • The total gain in one year is approximately 912.5 pounds, not 1,185 pounds. This statement is inaccurate.

4. It gains 365 pounds in 913 days.

   • In 913 days at 2.5 pounds/day, the total gain would be 913 * 2.5 = 2,282.5 pounds. This statement is inaccurate.

Based on this analysis, the only accurate interpretation of the slope is:

It gains 5 pounds every 2 days.