1.10 Numerical Methods (A-level only)

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Question 48

The concentration of a bio-pollutant in a nature reserve's lake is modeled by

75\left(\frac{t}{20}\right)^3 - 15\left(\frac{t}{20}\right)^4

where $C$ is the concentration in parts per billion (ppb) and $t$ is the number of years since 1 January 2010.

ai.

The model predicts that the pollutant concentration will eventually return to zero at a time $T$ . Show that $T$ satisfies the equation

\sqrt[3]{100T^2 + \frac{128\,000}{T}}

[3]

aii.

Use the iterative formula $000Tn3T_{n+1} = \sqrt[3]{100T_n^2 + \frac{128\,000}{T_n}}$ , with $T_0 = 50$ , to find the values of $T_1, T_2,$ and $T_3$ to three decimal places.

[3]

aiii.

Explain the relevance of using $T_0 = 50$ in terms of the date.

[1]

A neutralizing agent is introduced, and its effectiveness in reducing current pollutant levels is modeled by the supply function

\times 1.08^t

Use the models to show that the concentration $C$ and the neutralizing supply $S$ will be equal during the year 2075.

[4]

1.10 Numerical Methods (A-level only)

Question 48

Markscheme

1.10 Numerical Methods (A-level only)

Question 48

Markscheme

1.10 Numerical Methods (A-level only)

Question 48

1.10 Numerical Methods (A-level only) Questions

1.10 Numerical Methods (A-level only)

Question 48

1.10 Numerical Methods (A-level only) Questions