Lesson F2

F2 Exponential model and the gradient of e to the kx Quiz: AQA Maths, Unit 6

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F2, Exponential model and the gradient of e to the kx: 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. What is the derivative of e^(kx) with respect to x?

    • e^(kx)/k
    • k x e^(kx - 1)
    • e^x / k
    • k e^(kx)

  2. What is the gradient of y = e^(3x) at x = 0?

    • 0
    • e^3
    • 1
    • 3

  3. What is the rate of change of y = e^(kx) proportional to?

    • The product kx
    • Its current value
    • The value x
    • The constant k

  4. Find dy/dx for y = 5e^(-2x).

    • 10e^(-2x)
    • -2e^(-2x)
    • 5e^(-2x)
    • -10e^(-2x)

  5. What happens to y = A e^(kx) as x increases, where A > 0 and k > 0?

    • It approaches zero
    • It approaches infinity
    • It approaches A
    • It remains constant

  6. The curve y = e^(2x) passes through the point where y = 4. What is the gradient there?

    • 8
    • 2
    • 4
    • 16

  7. For y = e^(kx), the gradient at x = ln 2 / k is which value?

    • k
    • 2
    • ln 2
    • 2k

  8. A population is modelled by P = 100 e^(0.05t), with t in years. What is dP/dt when t = 0?

    • 0.05
    • 100
    • 105
    • 5

  9. A quantity satisfies N = 50 e^(0.2t). What is the rate of change of N when N = 100?

    • 20
    • 0.2
    • 10
    • 50

  10. A temperature model is T = 20 + 60 e^(-0.1t). What is dT/dt at t = 0?

    • 6
    • -0.1
    • -60
    • -6

  11. A car value is V = 12000 e^(-0.15t) pounds, with t in years. What is the initial rate of change of V?

    • -12000 pounds per year
    • -0.15 pounds per year
    • 1800 pounds per year
    • -1800 pounds per year

  12. What is the sign of the gradient of y = e^(-kt) for k > 0?

    • Always positive
    • Always zero
    • Always negative
    • Positively increasing

  13. For y = 3e^(2x), find the gradient at the point where y = 6.

    • 3
    • 12
    • 6
    • 24

  14. Which function satisfies dy/dx = 2y with y = 5 when x = 0?

    • y = 5x^2
    • y = 2e^(5x)
    • y = 10e^x
    • y = 5e^(2x)

  15. A quantity Q = Q0 e^(-kt) halves in time T. Which expression gives T?

    • T = 2k
    • T = k ln(1/2)
    • T = ln 2 / k
    • T = k / ln 2

  16. For y = e^(kx), the gradient at x = 2 equals 3 times the value of y there. What is k?

    • 2
    • 3
    • 6
    • 1/3

  17. Why does an exponential model overestimate population growth over long time periods?

    • Birth rates increase
    • Gradient is zero
    • Resources are limited
    • Death rates decrease

  18. The gradient of y = e^(kx) at the point (0, 1) is 4. What is k?

    • e^4
    • 1/4
    • ln 4
    • 4

  19. For y = e^(3x), find d^2y/dx^2.

    • e^(9x)
    • 6e^(3x)
    • 9e^(3x)
    • 3e^(3x)

  20. A quantity doubles every 5 years and follows Q = Q0 e^(kt). What is k to 3 significant figures?

    • 0.322
    • 5 ln 2
    • 0.400
    • 0.139

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