When cardiac tissue is damaged, troponin I is released into the blood. You are developing a diagnostic

blood test to detect and quantify troponin I. In a test tube, you immobilize $1$ picomole of an antibody

fragment that binds troponin with $5nM$ affinity. You add $100L$ of a blood sample containing $100nM$

troponin and incubate extensively to nearly reach equilibrium. You then remove the blood and wash away

the unbound molecules, leaving the tube sitting in $1mL$ of buffered saline solution, which is sufficient to

neglect re$-$binding of dissociated troponin.

a$.$ How much time passes before $10\%$ of the bound troponin has dissociated from the adsorbed antibody?

b$.$ How would your answer differ if you used an antibody with $0\mathrm{.}5nM$ affinity?