Logarithmic graphs and modelling growth and decayEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Linearise y=ax^{n}.
Linearise y=kb^{x}.
A \log{10}y against \log{10}x line has intercept 0.6. Find a.
A \log{10}P against t line has gradient 0.30. Find b.
What is the initial value in N=Ae^{kt}?
What does k<0 in N=Ae^{kt} mean?
What does k0 in N=Ae^{kt} mean?
Which graph is straight for N=Ae^{kt}?
Doubling time for N=Ae^{kt}?
Half-life for N=Ae^{-kt} with k0?
Solve 40e^{-0.25t}=10.
State one limitation of exponential growth for a population.
Suggest a refinement of an exponential population model.

Exam questions on Logarithmic graphs and modelling growth and decay

Experimental data for two variables $x$ and $y$ are modelled by $y=ax^{n}$ , where $a$ and $n$ are constants. When $\log_{10}y$ is plotted against $\log_{10}x$ , the points lie on a straight line with gradient $2.5$ and vertical-axis intercept $0.6$ .
Use the model to find the value of $y$ when $x=4$ , giving your answer to 3 significant figures.2 marks
Experimental data for two variables $t$ and $P$ are modelled by $P=kb^{t}$ , where $k$ and $b$ are constants. When $\log_{10}P$ is plotted against $t$ , the points lie on a straight line with gradient $0.30$ and vertical-axis intercept $1.20$ .
Find the value of $k$ , to 3 significant figures, and hence write down the model for $P$ in terms of $t$ .2 marks
The concentration, $C$ mg per litre, of a drug in a patient's blood $t$ hours after an injection is modelled by $C=40e^{-0.25t}$ for $t\geq0$ .
(i) State the concentration immediately after the injection. (ii) Find the concentration 6 hours after the injection, 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).