Lesson F7

F7 Exponential growth and decay in modelling Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F7, Exponential growth and decay in modelling: 20 multiple choice questions for the AQA Maths (7357), Unit 6: Exponentials and logarithms, written with Revision Ninja.

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The 20 questions

  1. Which expression describes exponential decay?

    • y = A e^(-kt) with A > 0 and k > 0
    • y = A e^(kt) with A > 0 and k > 0
    • y = At + k with k > 0
    • y = A t^k with k > 0

  2. In continuous compound interest at annual rate r, what is the amount after t years from principal P?

    • P + rt
    • P e^(rt)
    • P(1 + r)^t
    • P r^t

  3. Which limitation applies to an exponential growth model of a population?

    • It ignores limited resources, so it eventually overestimates the population
    • It predicts negative populations for all values of t
    • It is valid only for populations below 10
    • It predicts that the population stays constant forever

  4. A radioactive substance has half-life 5 years. What fraction remains after 10 years?

    • 1/2
    • 1/5
    • 1/10
    • 1/4

  5. Which quantity is constant for an exponential decay process?

    • The half-life
    • The amount remaining after a fixed time
    • The amount removed each year
    • The gradient at time zero for all substances

  6. A drug concentration is C = 80 e^(-0.2t) mg/L, with t in hours. What is the concentration after 5 hours?

    • 5.9 mg/L
    • 64.0 mg/L
    • 29.4 mg/L
    • 16.0 mg/L

  7. A sum of 1000 pounds is invested at 4% per year compounded continuously. What is its value after 10 years?

    • 1400.00 pounds
    • 1040.81 pounds
    • 1491.82 pounds
    • 1480.24 pounds

  8. A population of 5000 grows continuously at 2% per year. What is its rate of growth when the population is 6000?

    • 120 per year
    • 6000 per year
    • 0.02 per year
    • 100 per year

  9. A quantity is N = 200 e^(-0.3t). After approximately how long does N halve?

    • 0.69
    • 0.15
    • 2.31
    • 3.33

  10. A population is y = 50 e^(0.1t), with t in years. What is the doubling time to 2 decimal places?

    • 3.47 years
    • 5.00 years
    • 20.00 years
    • 6.93 years

  11. A model y = 1000 e^(kt) gives y = 2000 when t = 5. What is k to 3 decimal places?

    • 0.139
    • 0.035
    • 0.200
    • 0.693

  12. Which refinement makes an exponential decay model of drug concentration more realistic?

    • Changing the sign of the exponent to make the model grow
    • Replacing the exponential with a linear function of time
    • Using a power law so that the rate of decay becomes constant
    • Including repeated doses so that the concentration is topped up rather than falling to zero indefinitely

  13. A bacteria culture doubles every 3 hours and is modelled as N = N0 e^(kt). Which expression gives k?

    • k = ln 3 / 2
    • k = ln 2 / 3
    • k = 2/3
    • k = 3/ln 2

  14. A population model P = P0 e^(0.02t) predicts a 20% increase at what time t, to 2 decimal places?

    • 6.00 years
    • 10.00 years
    • 9.12 years
    • 0.18 years

  15. Under an exponential decay model with k = 0.5 per year, after what time is the quantity 1% of its initial value?

    • 4.61 years
    • 2.00 years
    • 9.21 years
    • 50.00 years

  16. A cooling model is T = 20 + 80 e^(-0.05t) degrees. What is the long-run temperature the model approaches?

    • 80 degrees
    • 100 degrees
    • 0 degrees
    • 20 degrees

  17. A model N = 500 e^(0.1t) predicts N = 1500 at what time t, to 2 decimal places?

    • 5.49
    • 15.00
    • 10.99
    • 1.10

  18. An exponential model of a population of 100 reaches 400 at t = 10. What is the growth constant k to 3 decimal places?

    • 0.693
    • 0.040
    • 0.139
    • 0.400

  19. Why might a logistic growth model be preferred to an exponential growth model for a population?

    • The population never changes in any model of growth
    • The data show a constant absolute increase in each period
    • Growth is limited by a carrying capacity, so the rate slows as the population approaches a maximum
    • Growth is always faster than exponential at every time

  20. A sample falls from 80 units to 10 units in 6 hours under exponential decay. What is its half-life?

    • 2 hours
    • 1 hour
    • 6 hours
    • 3 hours

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