An industrial chemical reactor is powered down for maintenance. At the moment the shutdown sequence begins, the secondary containment vessel holds 85 liters of cooling fluid. However, fluid continues to trickle from the cooling jackets into this vessel.
In the first minute after shutdown, 750 milliliters of fluid trickles into the vessel. In each subsequent minute, the volume of fluid trickling into the vessel decreases by 8%.
During the n n\,nth minute after shutdown, the volume of fluid trickling into the vessel is Rn R_n\,Rn milliliters.
Determine the value of R2R_2R2.
Explain why Rn=A×0.92n−1R_n = A \times 0.92^{n-1}Rn=A×0.92n−1 and state the value of the constant AAA.
Calculate the total increase in the volume of fluid in the containment vessel 15 minutes after the shutdown sequence begins. Give your answer to the nearest milliliter.
Assuming no fluid is lost from the containment vessel, find the maximum total volume of fluid it will eventually contain.
After a long period of time, the flow of fluid stops. Provide two practical reasons why the actual volume in the vessel might differ from the theoretical maximum calculated in part (d).
178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.