Exponential Growth & Decay (Cambridge O Level Maths)

The ideas of compound interest and depreciation can be applied to other (non-money) situations, such as increasing or decreasing populations.

 

What is exponential growth?

• When a quantity grows exponentially it is increasing from an original amount, P, by r % each year for n years
• Some questions use a different timescale, such as each day, or each minute
• Real-life examples of exponential growth include population increases, bacterial growth and the number of people infected by a virus
• The same formula from compound interest is used
• Final amount of the quantity is

• Substitute values of P, r and n from the question into the formula to find the final amount

 

What is exponential decay?

• When a quantity exponentially decays it is decreasing from an original amount, P, by r % each year for n years
• Some questions use a different timescale, such as each day, or each minute
• Real-life examples of exponential decay include the temperature of hot water cooling down, the value of a car decreasing over time and radioactive decay (how radioactive a substance is over time)
• The same formula from compound interest is used, but with +r replaced by -r
• Final amount of the quantity is

• Substitute values of P, r and n from the question into the formula to find the final amount

 

How do I use the exponential growth & decay formula?

• To find a final amount, substitute the values of P, r and n (from the question) into the formula
• If the final amount is given in the question, F, set the whole formula equal to this final amount

• Some questions then ask to find P, r or n
• To find P or r, rearrange the formula to make P or r the subject (for r, one of the steps involves taking an nth root)
• To find n, use trial and improvement (test different whole-number values for n until both sides of the equation balance)