Exponential growth and decay models: OCR MEI A‑Level Maths questions

OCR MEI A-Level Maths past-paper questions on 6.5 Exponential growth and decay models, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 16 questions on Exponential growth and decay models, as a list

June 2025, Paper 3, Q7 (9 marks): A group of scientists is studying how a population of insects grows in the laboratory. At the start of the study, there are 48 insects. At the end of the first
June 2025, AS Paper 1, Q12 (13 marks): A student dissolves 0.5 kg of salt in a bucket of water. Water leaks out of a hole in the bucket so the student lets fresh water flow in so that the bucket stay
June 2024, Paper 1, Q10 (10 marks): Zac is measuring the growth of a culture of bacteria in a laboratory. The initial area of the culture is 8 cm2. The area one day later is 8.8 cm2. , where A cm2
June 2023, Paper 1, Q11 (10 marks): The height h cm of a sunflower plant t days after planting the seed is modelled by h a b ln t = + for t 9 , where a and b are constants. The sunflower is 10 cm
June 2023, Paper 3, Q9 (9 marks): A small country started using solar panels to produce electrical energy in the year 2000. Electricity production is measured in megawatt hours (MWh). For the pe
June 2023, AS Paper 1, Q10 (7 marks): Layla invests money in the bank and receives compound interest. The amount £L that she has after 1 023t t years is given by the equation L 2800 . . = # (a) (i)
June 2022, Paper 1, Q14 (13 marks): Alex places a hot object into iced water and records the temperature i °C of the object every minute. e kt The temperature of an object t minutes after being pl
November 2021, Paper 3, Q5 (8 marks): x 5 (a) The diagram shows the curve y e . = y x O On the axes in the Printed Answer Booklet, sketch graphs of y against x, d (i) [1] x d y against y. d (ii) [2]
November 2021, AS Paper 1, Q11 (10 marks): On the day that a new consumer product went on sale (day zero), a call centre received 1 call about it. On the 2nd day after day zero the call centre received 3
November 2021, AS Paper 2, Q5 (7 marks): In 2019 scientists developed a model for comparing the ages of humans and dogs. According to the model, Y = AlnX + B where X = dog age in years and Y = human ag
November 2020, Paper 3, Q6 (12 marks): (a) (i) Write down the derivative of ekx, where k is a constant. 6 [1] (ii) A business has been running since 2009. They sell maths revision resources online. G
November 2020, AS Paper 2, Q11 (10 marks): - . 11 A car is travelling along a stretch of road at a steady speed of 11ms 1 The driver accelerates, and t seconds after starting to accelerate the speed of t
June 2019, AS Paper 2, Q9 (10 marks): In 2012 Adam bought a second hand car for £8500. Each year Adam has his car valued. He believes that there is a non‑linear relationship between t, the time in y
June 2018, Paper 2, Q16 (11 marks): In the first year of a course, an A-level student, Aaishah, has a mathematics test each week. The night before each test she revises for t hours. Over the cours
June 2018, Paper 3, Q5 (11 marks): A social media website launched on 1 January 2017. The owners of the website report the number of users the site has at the start of each month. They believe th
June 2018, AS Paper 2, Q12 (10 marks): In an experiment 500 fruit flies were released into a controlled environment. After 10 days there were 650 fruit flies present. Munirah believes that N, the num

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