MathsYears 12–13Exponentials and Logarithms

Exponential functions and modelling

Sketch and use exponential functions including e^x; model growth and decay; use ln for solving

What you'll learn

  1. 1

    Exponential functions grow super fast — like a virus spreading or money earning interest. Imagine a single penny that doubles every day — day 1 you have 1p, day 2 you have 2p, day 3 you have 4p, and by day 10 you have over £5!

  2. 2

    If you start with 1 penny and it doubles every day, how many pennies do you have on day 4?

  3. 3

    Let's model a population of 100 bacteria that triples every hour. What's the formula?

  4. 4

    Use the number line to see how a population of 50 bacteria that doubles every hour grows. Jump to hour 4.

  5. 5

    A car loses 20% of its value each year (decays by 0.8 each year). If it starts at £20,000, which formula models its value after x years?

  6. 6

    Plot the points for y = 2^x for x = 0, 1, 2, 3 on this bar chart — see how it shoots up!

  7. 7

    Which graph shape shows exponential growth?

Practise Exponential functions and modelling with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.