| Exam Board | AQA |
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| Module | AS Paper 2 (AS Paper 2) |
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| Session | Specimen |
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| Marks | 5 |
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| Topic | Differentiating Transcendental Functions |
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9 A curve has equation \(y = \mathrm { e } ^ { 2 x }\)
Find the coordinates of the point on the curve where the gradient of the curve is \(\frac { 1 } { 2 }\) Give your answer in an exact form.
[0pt]
[5 marks]
David has been investigating the population of rabbits on an island during a three-year period.
Based on data that he has collected, David decides to model the population of rabbits, \(R\), by the formula
$$R = 50 \mathrm { e } ^ { 0.5 t }$$
where \(t\) is the time in years after 1 January 2016.