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The table shows the number of calories in different servings of ice cream. Find and interpret the average rate of change on the interval [2,10].

serving (ounces) 0 2 5 6 9 10
calories 0 68 172 208 301 340

1 Answer

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The average rate of change in calories per ounce on the interval [2,10] for the given ice cream servings is approximately 23 calories per ounce. This indicates an average increase of 23 calories for each additional ounce of ice cream consumed within the specified range.

The average rate of change in calories per ounce over the interval [2,10] provides valuable insights into the calorie density of the ice cream servings. By calculating the difference in calories between the two endpoints of the interval (from 2 to 10 ounces) and dividing it by the corresponding difference in ounces, we find that the average rate of change is approximately 23 calories per ounce. This indicates that, on average, each additional ounce of ice cream within this range contributes an extra 23 calories.

In practical terms, the interpretation is that as the serving size increases from 2 to 10 ounces, consumers can expect an average calorie increment of 23 for every additional ounce consumed. This insight is valuable for individuals monitoring their caloric intake or making dietary decisions based on portion sizes, providing a quantitative measure of the calorie content associated with incremental increases in ice cream servings within the specified range.

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