To test an individual\'s use of a certain mineral, a researcher injects small am

Question

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 in 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(6t + 2)^-1/2. Find the rate of change of the mineral level with respect to time for 0 days. The rate of change of the mineral level with respect to time for 0 days is approximately milligrams per cubic centimeter per day. (Round to two decimal places as needed.)

Explanation / Answer

C(t) = (1/2)*(6t + 2)^-0.5

rate of change will be given by:

C'(t) = d[C(t)]/dt

we know that

d(f^n)/dt = n*f^(n-1)*f'

C'(t) = d[(1/2)*(6t + 2)^-0.5]/dt

= (1/2)*(-1/2)*(6t + 2)^(-1/2 - 1)*(6*1 + 0)

= (-1/4)*6*(6t + 2)^(-3/2)

at t = 0, rate of change in mineral level will be:

C'(0) = (-3/2)*(6*0 + 2)^(-3/2)

C'(0) = -0.53

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