To test an individual's use of a certain mineral, a researcher injects small amount of a radioactive form of that mineral into the person's bloodstream. The mineral remaining is the bloodstream is measured each day for several days. Suppose the amount of the mineral remaining in the bloodstream (in milligrams per cubic centimeter) t days after the initial injection is approximated by:

C (t) = 1/2 (4t + 4) - 1/2

Find the rate of change of the mineral level with respect to time for 7.5 days.

Question

Mathematics

Kayden Wise

8 April, 03:42

To test an individual's use of a certain mineral, a researcher injects small amount of a radioactive form of that mineral into the person's bloodstream. The mineral remaining is the bloodstream is measured each day for several days. Suppose the amount of the mineral remaining in the bloodstream (in milligrams per cubic centimeter) t days after the initial injection is approximated by:

C (t) = 1/2 (4t + 4) - 1/2

Find the rate of change of the mineral level with respect to time for 7.5 days.

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Answers (1)

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Damari Olsen · Answer 1

dC/dt = 2 mg*cm³/s

Step-by-step explanation:

Given

C (t) = (1/2) * (4t + 4) - (1/2)

we apply dC/dt as follows

dC/dt = d ((1/2) * (4t + 4) - (1/2)) / dt = (1/2) * (4) = 2

⇒ dC/dt = 2 mg*cm³/s