1. Exponential Growth & Decay
Core 4 Maths with Liz

2. Objective Prior Knowledge
By the end of the lesson you should be able to…
Understand exponential growth & decay
Solve exponential equations
be familiar with the exponential curve.
Prior Knowledge
Solving equations using natural logs.

3. The amount of money in a bank account with a high interest rate.
Exponential Growth
If something grows exponentially, that means that the rate at which it gets bigger increases proportionally to the growing total number or size.
Examples:
The amount of money in a bank account with a high interest rate.
The amount of rabbits on a farm.
The amount of “walkers” after a zombie outbreak.

4. Exponential Growth
Therefore, A represents the starting value before any time has gone by.

5. Example 1 – Exponential Growth
A man is bitten by a zombie and is immediately infected with bacteria in his blood. The bacteria growth rate is
Once the bacteria level reaches 1,000,000, the infection will be unstoppable and the man will become zombified within the next 24 to 36 hours. How long will it take for him to reach the point of no return?

6. The temperature of a freshly poured cup of coffee.
Exponential Decay
If something decays exponentially, that means that as the total size or population gets smaller, so does the rate at which is it decreasing.
Examples:
The value of a sports car.
The temperature of a freshly poured cup of coffee.
The population size of the human race in the first 6 months of a zombie apocalypse.

7. Exponential Decay

8. Example 2 – Exponential Decay

9. Example 3 – Exponential Decay

10. Exam Question June 2013 (part a only)

11. June 2013 – Working out When t = 0,
There were 50 rodents at the start of the investigation.

12. June 2013 – working out When t = 24,
There were approximately 345 rodents after 24 weeks.

13. June 2013 – working out
When N = 400,

14. Independent Study