1) The document discusses growth and decay functions using two examples: Harry's hedge, which grows 7% annually, and Alisha's allotment, which yields less potatoes each year due to a 16% annual decay. 2) Growth functions take the form f(n) = f0(A)n, where A is greater than 1, while decay functions take the same form but with A less than 1. 3) Both growth and decay functions are examples of simple exponential functions.

1. Block 3
Growth and Decay

2. What is to be learned?
• How to recognise simple growth or decay
functions

3. Harry’s hedge is 40 cm tall
His special fertilizer increases its height by 7% p.a.
Height after 1 year 1.07 X 40
Height after 2 years 1.07 X 1.07 X 40
Height after 10 years
1.072
X 40
1.0710
X 40
Height after n years H(n) = 1.07n
X 40
or 40 X 1.07n
Growth function
Original Value Variable

4. Alisha’s allotment yields 120 kg of potatoes
Sadly its harvest is reducing by 16% p.a.
Tatties after 1 year 0.84 X 120
Tatties after 2 years
Tatties after 10 years
0.842
X 120
0.8410
X 120
Tatties after n years P(n) = 0.84n
X 120
or 120 ( 0.84n
)
Decay function
Original Value Variable
less than 1

5. Graphs
n
f(n)
f(n) = f0 (A)n
Growth function
A > 1

6. Graphs
n
f(n)
f(n) = f0 (A)n
Decay function
A < 1
both are exponential functions
Growth function
A > 1

7. Simple Exponential Functions
Written in form f(n) = f0(A)n
f0 is initial value
If A > 1
If A < 1
Growth Function
Decay Function

8. Graphs
n
f(n)
Growth
Decay