Exam 1

  1. Question

    The function y=H(t)y=H(t) measures the amount of iron in Sarah’s bloodstream (in milligrams) where tt is measured in minutes since she ingested an iron supplement. Suppose H(21)=6.7H^'(21)=6.7.

    Select each of the true statements from the following:


    1. Twenty-one minutes after ingesting the iron supplement, Sarah had 6.7 milligrams of iron in her bloodstream.
    2. On average, the amount of iron in Sarah’s bloodstream increased by 6.7 milligrams each minute over the first 21 minutes since she ingested the iron supplement is an interpretation of H(21)H(0)21 \frac{H(21) - H(0)}{21}
    3. Twenty-one minutes after ingesting the iron supplement, the amount of iron in Sarah’s bloodstream was growing at a rate of 6.7 milligrams per minute.

    Solution

    1. False. The amount of iron in Sarah’s bloodstream is given by the function H(t)H(t). This statement would be the correct interpretation of H(21)=6.7H(21)=6.7
    2. True. The average rate of change of H(t)H(t) over the first 21 minutes (i.e., over the interval [0,21][0,21] is H(21)H(0)21 \frac{H(21) - H(0)}{21}
    3. True. This is the correct interpretation of H(21)=6.7H(21)=6.7