A marine biologist is monitoring the rate of oxygen consumption, RRR (measured in mg/L/h), by a specific coral species in a research tank. The rate can be modelled by the equation
R=1.2+2t−4+24−t−0.5(t−4)2,1≤t≤7 R = 1.2 + 2^{t-4} + 2^{4-t} - 0.5(t-4)^2, \quad 1 \le t \le 7 R=1.2+2t−4+24−t−0.5(t−4)2,1≤t≤7where ttt is the time in hours after the start of the observation.
A table of values for ttt and RRR is shown below, with values of RRR given to 4 significant figures where appropriate.
| Time, ttt (h) | 2 | 2.5 | 3 | 3.5 | 4 |
|---|---|---|---|---|---|
| Rate, RRR (mg/L/h) | 3.257 | 3.2 | 3.2 |
Use the given equation to complete the table, giving the values of RRR to 4 significant figures where appropriate.
The total amount of oxygen consumed by the coral during the interval between t=2t = 2t=2 and t=4t = 4t=4 can be estimated by calculating the area under the curve. Use the trapezium rule, with all the values of RRR in the completed table, to find an estimate for this total oxygen consumption. Give your answer to 2 decimal places.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
