An industrial vat used for fermentation is being cleaned, and the primary supply is shut off. At the moment of shut-off, the vat contains 450 litres of liquid. However, residual fluid continues to drip from the overhead processing coils into the vat.
In the first minute after the supply is shut off, 800 millilitres of liquid drips into the vat. In each subsequent minute, the volume of liquid dripping into the vat reduces by 16%.
During the n n\,nth minute after the supply is turned off, the volume of liquid dripping into the vat is Wn W_n\,Wn millilitres.
Find W2W_2W2.
Explain why Wn=A×0.84n−1W_n = A \times 0.84^{n-1}Wn=A×0.84n−1 and state the value of AAA.
Find the total increase in the volume of liquid in the vat 15 minutes after the supply is shut off. Give your answer to the nearest millilitre.
Assuming no liquid is lost or added from other sources, calculate the maximum possible total volume of liquid in the vat.
After a significant period of time has passed, the dripping has ceased. Give two reasons why the final volume of liquid in the vat might not reach the theoretical maximum calculated in part (d).
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.