Logarithmic graphs and modellingEdexcel International A Level Maths: Mind map

Exam questions on Logarithmic graphs and modelling

1. A scientist believes that two variables are related by $y=ax^{n}$, where $a$ and $n$ are constants. She plots $\lg y$ against $\lg x$ and obtains a straight line with gradient $3$ that crosses the vertical axis at $2$.
   Find the value of $y$ when $x=4$.2 marks
2. Two variables are related by $y=kb^{x}$, where $k$ and $b$ are positive constants. A graph of $\lg y$ against $x$ is a straight line through the points $(0,\,0.6)$ and $(5,\,2.1)$.
   Use the model to find the value of $y$ when $x=8$.2 marks
3. The variables $x$ and $y$ are related by $y=ax^{n}$. A graph of $\lg y$ against $\lg x$ is a straight line through the points $(0.2,\,0.8)$ and $(0.6,\,1.6)$.
   Show that $n=2$ and find the value of $a$ to 3 significant figures.3 marks