(a)[1]
Use logarithms to demonstrate that the gradient of the straight line is $\frac{3}{2\ln a}$.
(b)[4]
Using the fact that the straight line passes 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 $y$ are related by $a^{2y} = e^{3x+k}$, with $a$ and $k$ constant. A graph of $y$ 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 $2y\ln a = 3x + k$ and then conclude that the gradient is $\frac{3}{2\ln a}$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI