Exponential growth and decayAQA A-Level Maths: Flashcards

What these 13 flashcards ask

General exponential model with base e?
What does the sign of k tell you in y=Ae^{kt}?
How are y=Ae^{kt} and y=Ab^t related?
Why do exponential models suit growth and decay?
Formula for continuous compound interest?
Doubling time for y=Ae^{kt}, k0?
Half-life for y=Ae^{-\lambda t}?
Is half-life constant? Why?
Method to find when 80e^{-0.05t}=10?
Equivalent annual rate for continuous rate r?
Main limitation of an exponential population model?
A refinement to an exponential growth model?
What is a carrying capacity?

Exam questions on Exponential growth and decay

The mass $M$ grams of a radioactive isotope, $t$ days after it was first measured, is modelled by $M=80\mathrm{e}^{-0.05t}$ .
Find the time taken for the mass of the isotope to fall to 10 g. Give your answer to 3 significant figures.2 marks
£6000 is invested in an account with interest compounded continuously, so that after $t$ years the value of the investment is £ $V$ , where $V=6000\mathrm{e}^{0.04t}$ .
Find the equivalent annual rate of interest, as a percentage to 3 significant figures, that would give the same value after each full year.2 marks
A patient is given a dose of a drug. The concentration $C$ of the drug in the blood, in mg per litre, $t$ hours after the dose is modelled by $C=12\mathrm{e}^{-0.3t}$ .
The drug is only effective while the concentration is at least 2 mg per litre. Find how long after the dose the drug stops being effective, giving your answer in hours 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).