Which expression approximately represents the number of hours, h, after administration if the remaining medication in the patient's bloodstream is 421 milligrams?

Answer 1

So, this sounds like a case of "the rate of change of the amount is directly proportional to the amount" :

dA/dt = kA

The solutions to this differential equation look like

A(t) = A₀ e^kt

You have two unknowns - - A₀ the initial amount, and k the decay coefficient (decay here because I believe k would be negative since the amount of medication in the blood stream generally decreases over time. You have not given me enough information to find those from your question. But we can still answer IN TERMS OF THOSE VARIABLES:

421 = A₀ e^kh where t is measured in hours, I'll say, and I need to solve for this particular "h" that I say is the number of hours it takes for the amount to be 421.

Little bit of algebra:

h = (1/k)ln(421/A₀ )

Good Luck!