3.3.4 Sequences and series (A-level only)

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Question 29

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.

[2]

The quantity of Enzyme B is being monitored over the same period. Given that:

2 hours after monitoring began there were 3200 units of Enzyme B
5 hours after monitoring began there were 2400 units of Enzyme B
the quantity of Enzyme B at the end of each hour is modelled as a geometric sequence

Find the equation of this model in the form

N = ab^t

where $N$ is the number of units of Enzyme B, $t$ hours after monitoring began, and $a$ and $b$ are constants. Give the value of $a$ and the value of $b$ to 2 significant figures.

[4]

When $t = T$ , the quantity of Enzyme A is equal to the quantity of Enzyme B.

Find, according to the models, the value of $T$ , giving your answer to one decimal place.

[4]

3.3.4 Sequences and series (A-level only)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Question 29

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.

[2]

The quantity of Enzyme B is being monitored over the same period. Given that:

2 hours after monitoring began there were 3200 units of Enzyme B
5 hours after monitoring began there were 2400 units of Enzyme B
the quantity of Enzyme B at the end of each hour is modelled as a geometric sequence

Find the equation of this model in the form

N = ab^t

where $N$ is the number of units of Enzyme B, $t$ hours after monitoring began, and $a$ and $b$ are constants. Give the value of $a$ and the value of $b$ to 2 significant figures.

[4]

When $t = T$ , the quantity of Enzyme A is equal to the quantity of Enzyme B.

Find, according to the models, the value of $T$ , giving your answer to one decimal place.

[4]

3.3.4 Sequences and series (A-level only)

Question 29

Markscheme

3.3.4 Sequences and series (A-level only)

Question 29

Markscheme

3.3.4 Sequences and series (A-level only)

Question 29

3.3.4 Sequences and series (A-level only) Questions

3.3.4 Sequences and series (A-level only)

Question 29

3.3.4 Sequences and series (A-level only) Questions