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.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.