In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The concentrations of two enzymes, Enzyme A and Enzyme B, are being monitored in a laboratory bioreactor. Initially, there are 800 units of Enzyme A.
A model predicts that the quantity of Enzyme A will increase by 6% each hour, so that the number of units of Enzyme A at the end of each hour forms a geometric sequence.
Find, according to the model, the number of units of Enzyme A in the bioreactor 12 hours after monitoring began. Give your answer to 3 significant figures.
The quantity of Enzyme B is being monitored over the same period. Given that:
Find the equation of this model in the form
N=abt N = ab^t N=abtwhere NNN is the number of units of Enzyme B, ttt hours after monitoring began, and aaa and bbb are constants. Give the value of aaa and the value of bbb to 2 significant figures.
When t=Tt = Tt=T, the quantity of Enzyme A is equal to the quantity of Enzyme B.
Find, according to the models, the value of TTT, giving your answer to one decimal place.
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.