3.4 Geometric Series

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In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

A laboratory is monitoring the mass of two newly synthesised isotopes, Alpha and Beta, during a stability experiment.

Initially, the mass of Isotope Alpha is 800 mg. A model predicts that the mass of Alpha will increase by 6% each year due to artificial enrichment, so that the mass at the end of each year forms a geometric sequence.

Find, according to the model, the mass of Isotope Alpha 10 years after monitoring began. Give your answer to 3 significant figures.

[3]

The mass of Isotope Beta is being monitored over the same period. Given that:

4 years after monitoring began, the mass was 3200 mg
9 years after monitoring began, the mass was 2100 mg
the mass of Isotope Beta at the end of each year is modelled as a geometric sequence

Find the equation of this model in the form $M = ab^t$ where $M$ is the mass of Isotope Beta, $t$ years after monitoring began, and $a$ and $b$ are constants. Give the value of $a$ and the value of $b$ to 2 significant figures.

[4]

At the time $t = T$ , the mass of Isotope Alpha is equal to the mass of Isotope Beta.

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

[5]

3.4 Geometric Series Questions

Practise Edexcel A Level Maths 3.4 Geometric Series with exam-style questions for A Level Maths. 27 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.