Moderate -0.8 This is a straightforward exponential decay question requiring only standard techniques: stating the model y = Ae^(kx), substituting given values to find k using logarithms, and solving another exponential equation. All steps are routine A-level procedures with no problem-solving insight needed, making it easier than average but not trivial due to the multi-step calculation.
Two variables, \(x\) and \(y\), are such that the rate of change of \(y\) with respect to \(x\) is proportional to \(y\). State a model which may be appropriate for \(y\) in terms of \(x\). [1]
The concentration, \(Y\) units, of a certain drug in a patient's body decreases exponentially with respect to time. At time \(t\) hours the concentration can be modelled by \(Y = Ae^{-kt}\), where \(A\) and \(k\) are constants.
A patient was given a dose of the drug that resulted in an initial concentration of 5 units.
After 4 hours, the concentration had dropped to 1.25 units. Show that \(k = 0.3466\), correct to four decimal places. [2]
The minimum effective concentration of the drug is 0.6 units. How much longer would it take for the drug concentration to drop to the minimum effective level? [3]
\begin{enumerate}[label=(\alph*)]
\item Two variables, $x$ and $y$, are such that the rate of change of $y$ with respect to $x$ is proportional to $y$. State a model which may be appropriate for $y$ in terms of $x$. [1]
\item The concentration, $Y$ units, of a certain drug in a patient's body decreases exponentially with respect to time. At time $t$ hours the concentration can be modelled by $Y = Ae^{-kt}$, where $A$ and $k$ are constants.
A patient was given a dose of the drug that resulted in an initial concentration of 5 units.
\begin{enumerate}[label=(\roman*)]
\item After 4 hours, the concentration had dropped to 1.25 units. Show that $k = 0.3466$, correct to four decimal places. [2]
\item The minimum effective concentration of the drug is 0.6 units. How much longer would it take for the drug concentration to drop to the minimum effective level? [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q14 [6]}}