Exponential growth and decay modelsEdexcel International A Level Maths: Mind map

Exam questions on Exponential growth and decay models

1. 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
2. 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
3. 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