Question 30

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:

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.

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.