Logarithmic graphs and modelling growth and decayEdexcel A-Level Maths: Mind map

Exam questions on Logarithmic graphs and modelling growth and decay

1. 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
2. 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
3. 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