(a)[1]
Apply logarithms to establish that the gradient of the straight line is $\frac{3}{2\ln a}$.
(b)[4]
Since the straight line goes through the points $(0.4, 0.95)$ and $(3.3, 3.80)$, determine the values of $a$ and $k$.
Mathematics 9709 · AS & A Level · Logarithmic and exponential functions
Logarithmic and exponential functions — practice question
The variables $x$ and $y$ obey the equation $a^y = e^{3x + k}$, with $a$ and $k$ as constants, and the graph of $y$ plotted against $x$ is a straight line.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or imply $2y\ln a = 3x + k$, then deduce that the gradient is $\dfrac{3}{2\ln a}$” …
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