Logarithmic graphs and modellingEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

Linear form of y=ax^{n} using \lg?
Linear form of y=kb^{x} using \lg?
For y=ax^n, what do you plot on each axis?
For y=kb^x, what do you plot on each axis?
For y=ax^n, what is the gradient and intercept of the line?
For y=kb^x, what is the gradient and intercept of the line?
How do you find a from the intercept c?
How do you find b from the gradient m?
State \lg(AB).
State \lg(A^p).
How do you find the gradient from two points (X1,Y1) and (X2,Y2)?
A line of \lg y against \lg x has gradient 2 and intercept 0.4. What is y?

Exam questions on Logarithmic graphs and modelling

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).