1.1. An exponential model of the form

$D=A{e}^{-kt}$

is used to model the concentration of a pain-relieving drug (D mg/ml) in a patient’s bloodstream $t$ hours after the drug was administered by injection.  $A$ and $k$ are constants.

The graph below shows values of $lnD$ plotted against $t$

Find estimates for the constants $A$and $k$.

1.2. Find the time, to the nearest minute, at which the rate of decrease of the concentration of the drug in the patient’s bloodstream is 12 mg/ml/hour.