Population growth and depreciation
A town's population grows by a fixed per cent each year, and a motorbike loses a fixed per cent of its value each year. Change the rate and the years, and see compound growth and compound depreciation.
Core concept
Growth by R% a year gives V = V₀(1 + R/100)^T; depreciation by R% a year gives V = V₀(1 − R/100)^T, the compound interest formula with a plus or a minus
Topic: Population growth and depreciation
A town of 50000 people grows by 5% a year. After one year it has 50000 × 1.05 people; the next year grows by 5% of that bigger number, just like compound interest. After T years the population is P = P₀(1 + R/100)^T. Things also lose value as they get older. A new motorbike costing Rs 200000 that depreciates by 15% a year is worth 85% of its value each year: V = V₀(1 − R/100)^T. Depreciation is the loss in value, V₀ − V.
What you will learn
- Calculate a population after compound growth.
- Calculate a value after compound depreciation.
- Find the increase or the loss over the years.
Before you start
- Know the compound amount formula, A = P(1 + R/100)^T.
Materials
- A notebook and a calculator
Equipment
- None
Procedure
- Record the town's population at 5% for 3 years.
- Make it 5 years and record.
- Change to the motorbike at 15% for 3 years and record.
How this simulation is simplified
- The rate stays the same every year; people moving in or out are left out.