(a)[3]
State the value of $k$ and determine the value of $a$ correct to $2$ significant figures.
(b)[2]
Find the time for $P$ to double. Give your answer correct to the nearest hour.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
A bacterial population, $P$, after $t$ hours is represented by $P = ae^{kt}$, where $a$ and $k$ are constants. In the diagram, the graph of $\ln P$ against $t$ is a straight line with gradient $\frac{1}{20}$ and it cuts the vertical axis at $(0, 3)$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State, or indicate, $\ln P=\ln a+kt$ (or $\ln a+k(\ln e)t$).” …
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