A large reservoir is contaminated with a chemical pollutant. The concentration, $P$ parts per billion (ppb), of the pollutant after $t$ days of treatment can be modelled by

P = P_0 e^{-kt}

where $P_0$ is the initial concentration and $k$ is a positive constant. The model is considered accurate for high concentrations.

It takes 22.5 days for the concentration of the pollutant to reach 40% of its initial value.

Determine the number of weeks required for at least 97% of the original pollutant to be removed.

Find the percentage of the initial concentration remaining after 4 weeks. Give your answer to two significant figures.

Explain why the model can only provide an estimate for the actual concentration observed.

Explain why the model is invalid in the very long run as $\to \infty$ .

A large reservoir is contaminated with a chemical pollutant. The concentration, $P$ parts per billion (ppb), of the pollutant after $t$ days of treatment can be modelled by

P = P_0 e^{-kt}

where $P_0$ is the initial concentration and $k$ is a positive constant. The model is considered accurate for high concentrations.

It takes 22.5 days for the concentration of the pollutant to reach 40% of its initial value.

Determine the number of weeks required for at least 97% of the original pollutant to be removed.

Find the percentage of the initial concentration remaining after 4 weeks. Give your answer to two significant figures.

Explain why the model can only provide an estimate for the actual concentration observed.

Explain why the model is invalid in the very long run as $\to \infty$ .

11.11 Modelling with Differential Equations

Question 27

Markscheme

11.11 Modelling with Differential Equations

Question 27

Markscheme

11.11 Modelling with Differential Equations

Question 27

11.11 Modelling with Differential Equations Questions

11.11 Modelling with Differential Equations

Question 27

11.11 Modelling with Differential Equations Questions