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
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
If you start with 1 penny and it doubles every day, how many pennies do you have on day 4?
- 3
Let's model a population of 100 bacteria that triples every hour. What's the formula?
- 4
Use the number line to see how a population of 50 bacteria that doubles every hour grows. Jump to hour 4.
- 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
Plot the points for y = 2^x for x = 0, 1, 2, 3 on this bar chart — see how it shoots up!
- 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.