Logarithmic graphsAQA A-Level Maths: Mind map

Exam questions on Logarithmic graphs

1. Variables $x$ and $y$ are related by $y=ax^n$, where $a$ and $n$ are constants. A graph of $\lg y$ against $\lg x$ is a straight line passing through the point $(0,0.6)$ on the vertical axis, with gradient $1.5$.
   Estimate the value of $y$ when $x=100$, giving your answer to 3 significant figures.2 marks
2. The number of cells $y$ in a culture $x$ days after the start is modelled by $y=kb^x$, where $k$ and $b$ are constants. A graph of $\lg y$ against $x$ is a straight line passing through $(0,2)$ and $(4,3.2)$.
   Use the model to estimate how many days it takes for the culture to reach 5000 cells. Give your answer to 3 significant figures.2 marks
3. Variables $x$ and $y$ are thought to satisfy $y=ax^n$, where $a$ and $n$ are constants. A graph of $\lg y$ against $\lg x$ has a line of best fit passing through the points $(0.60,1.38)$ and $(1.20,2.28)$.
   Show that $\lg y=n\lg x+\lg a$, and find the value of $n$.3 marks