Chapter 4.4, Problem 61E

Radioactive Iron Researchers found that the fraction of radioactive iron in one patient’s blood plasma could be describe by

$f\left(t\right)=0.981e^{-6.74t}+0.0163e^{-1.019t}+0.0031e^{-0.210t},$

where $t$ is the time in days after the iron was injected. Source: The Journal of Clinical Investigation.

a. Find the fraction of radioactive iron remaining and the rate that it was declining at (i) 6 hours, (ii) 1 day, and (iii) 5 days.

b. What is happening to the fraction of radioactive iron in the plasma as time goes on?

c. What is happening to the rate of change of the fraction of radioactive iron in the plasma as time goes on?

d. Calculate the value of each of the terms of $f\left(t\right)$ at (i) 6 hours, (ii) 1 day, and (iii) 5 days.

e. from your answer to part d, which terms is most important at (i) 6 hours, (ii) 1 day, and (iii) 5 days? Explain why this is happening, based on the values of coefficients of each terms and the coefficient of $t$ in each term.