1. What are Growth and decay?
In simple words, Growth refers to the increase in the number of things over a period of time & Decay refers to the decrease in the number of things over a period of time.
2. Compounded or Exponential Growth and Decay
Exponential growth is when a quantity increases more and more over periods of time.
The formula for exponential growth can be written as follows -
Where
Pn ⟶ amount after n periods
P0 ⟶ initial amount
n ⟶ numbers of periods
r ⟶ % rate of growth
Exponential decay is when a quantity decreases more and more over periods of time.
The formula for exponential decay can be written as follows -
Where
Pn ⟶ amount after n periods
P0 ⟶ initial amount
n ⟶ numbers of periods
r ⟶ % rate of growth
In GCSE previous years question you may find the equation given for exponential growth or decay in the format shown below:
V = 16000 × 0.75ˆt
0.75 here is nothing but (1 + r⁄100), if you compare with the above mentioned formula the rate of decay here is 25%. So don’t get scared by this because it is actually better and you just have to put in numbers to get your answer.
Let's dive into some examples to understand the concept better -
Example 1:
Mr. Charls invests £500 in a bond for 4 years which promises a compound interest rate of 5% per annum. What amount will Mr. Charles get after 4 years?
Example 2:
The population of country A in 2000 was 12 million which is decreasing by 8% every year. Assuming the rate remains constant over the years, how many people will reside in country A by 2010.
Example 3:
The value of a bicycle, £V, is given by
V = 135 × 0.8ˆn
Where n is the number of years after it is bought from new.
- Calculate the value of the bicycle when new.
2. Calculate the annual percentage decrease in the value of the bicycle.
3. Calculate the value of the bicycle after 5 years.
