Lesson 1.06i

1.06i Exponential modelling Quiz: OCR Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson 1.06i, Exponential modelling: 20 multiple choice questions for the OCR Maths (H240), Unit 6: Exponentials and Logarithms, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Which formula models continuous compound interest?

    • A = P(1 + r)^t
    • A = P e^(t/r)
    • A = P e^(rt)
    • A = P r e^t

  2. Which formula models radioactive decay with half-life T?

    • N = N0 (1/2)^(t T)
    • N = N0 (1/2)^(t/T)
    • N = N0 2^(t/T)
    • N = N0 e^(t/T)

  3. As time t increases, what value does y = A e^(-kt) approach for k > 0?

    • 0
    • 1
    • A
    • Infinity

  4. Which limit defines the mathematical constant e as n approaches infinity?

    • (1 + 1/n)
    • (1 + 1/n)^n
    • (1 + n)^(1/n)
    • (1 - 1/n)^n

  5. For N = N0 e^(-lambda t), what is the half-life T?

    • T = 2 / lambda
    • T = ln 2 / lambda
    • T = lambda / ln 2
    • T = ln(lambda) / 2

  6. Which parameter in a refined population model represents the maximum sustainable population size?

    • Half-life
    • Carrying capacity
    • Growth rate
    • Initial population

  7. What is £2000 invested at 4% continuous compound interest worth after 3 years?

    • £2254.99
    • £2250.00
    • £2249.73
    • £2240.00

  8. A sample of 80 g has half-life 5 years. How much remains after 15 years?

    • 40 g
    • 5 g
    • 10 g
    • 20 g

  9. A count N = 500 e^(-0.2t) decays. Roughly how long does it take to halve?

    • 0.69
    • 5.00
    • About 3.47
    • 2.50

  10. A population P = 1000 e^(0.05t) is modelled. What is its growth rate at t = 0?

    • 1000 per year
    • 50 per year
    • 1050 per year
    • 0.05 per year

  11. A drug concentration is C = 12 e^(-0.5t) mg/L. What is it after 2 hours?

    • 0.12 mg/L
    • 1.62 mg/L
    • 6.00 mg/L
    • 4.41 mg/L

  12. A car worth £20 000 depreciates by 15% each year. What is its value after 3 years?

    • £14 450.00
    • £12 282.50
    • £17 000.00
    • £11 000.00

  13. A quantity grows as e^(0.1t). What is its doubling time?

    • About 0.69 years
    • About 5.00 years
    • About 10.00 years
    • About 6.93 years

  14. A population doubles every 20 days under exponential growth. What is the growth constant k?

    • About 0.0500 per day
    • About 0.0347 per day
    • About 0.0200 per day
    • About 0.693 per day

  15. How long does N = 200 e^(0.3t) take to reach 1000?

    • About 5.37
    • 3.00
    • 1.61
    • 16.09

  16. A substance has a half-life of 30 years. What is its decay constant lambda?

    • About 0.0231 per year
    • About 0.6931 per year
    • About 0.0333 per year
    • About 20.79 per year

  17. Which expression gives the annual growth factor for a continuous growth rate of 5%?

    • 1.05^1
    • e^0.05
    • ln(0.05)
    • e^1.05

  18. In the exponential growth model y = A e^(kt), what does k represent?

    • Time elapsed
    • Growth rate
    • Initial value
    • Upper limit

  19. What is the initial value of N = 50 e^(0.02t)?

    • 50
    • 1
    • 0.02
    • 51

  20. A bacterial colony doubles every 4 hours. Which model gives the count N after t hours from N0?

    • N = N0 e^(4t)
    • N = N0 4^(t/2)
    • N = N0 2^(t/4)
    • N = N0 2^(4t)

All OCR Maths quizzes