Exponential growth and decayAQA A-Level Maths: Mind map

Exam questions on Exponential growth and decay

1. 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
2. £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
3. 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