Exponential growth and decay modelsEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

Write the general exponential growth/decay model.
What does A represent in N=Ae^{kt}?
What sign of k means growth? Decay?
If N=Ae^{kt}, what is \frac{dN}{dt}?
What is the doubling time for N=Ae^{kt}?
Solve e^{0.05t}=2.
What happens to 50e^{-0.02t} as t\to\infty?
What happens to 400e^{0.05t} as t\to\infty?
Find k if N=100 at t=0 and N=150 at t=2.
Long-term value of \theta=20+70e^{-0.04t}?
Why is B+Ce^{-kt} often a better model than Ce^{-kt} for cooling?
What does 'initial' mean in a modelling question?

Exam questions on Exponential growth and decay models

The population $P$ of a colony of bacteria is modelled by $P=400e^{0.05t}$ , where $t$ is the time in hours after the start of observation.
Find the time taken for the population to double, giving your answer in hours to 3 significant figures.2 marks
The mass $m$ grams of a radioactive isotope is modelled by $m=50e^{-0.02t}$ , where $t$ is the time in years after the isotope is first measured.
Find the time taken for the mass to fall to 20 g, giving your answer in years to 3 significant figures.2 marks
A cup of tea is poured at time $t=0$ and left to cool in a room. Its temperature $\theta\,^\circ$ C after $t$ minutes is modelled by $\theta=20+70e^{-0.04t}$ .
Find the initial temperature of the tea, and the time taken for the tea to cool to $50^\circ$ C, giving the time 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).