Theory:

In our day to day life, we observe that there are some situations or things that increase in magnitude over a period of time.
      Example:
    • The population of a state/country
    • The value of the property
    • Investment returns
    • The growth of the cell
    • The depreciation in the values of machines, vehicles, etc.,
Similar to the compound interest the above mentions things also will increase over a period. Using particular formulae we can also calculate those things. And we will learn all about this in this chapter.
1. Increase in Growth:
Population Growth:
 
Type 1)
 
Growth after \(n\) years:
Let \(P\) be the population of a city or state at the beginning of a certain year and the population grows at a constant rate of \(r \%\) per annum.
 
Therefore:
Population after \(n\) years \(A\) =P(1+r100)n
Type 2)
 
Growth grows at different rate:
Let \(P\) be the population of a city or state at the beginning of a certain year and the population grows at a constant rate of \(r_1 \%\) in the first year and, \(r_2 \%\) in the second year.
 
Population after \(n\) years \(A =\) P(1+r1100)(1+r2100)(1+r3100).......(1+rn100).
Type 3)
 
Growth decreases:
Let \(P\) be the population of a city or state at the beginning of a certain year and the population decreases at the rate of \(r \%\) per annum.
 
Therefore:
 
Population after \(n\) years A=P(1r100)n.
Important!
We can also use the above formulae to the growth of cells in a particular period at a particular rate and the value of land increased or decreased at a particular time at a particular rate.
2. Depreciation:
To find Depreciation if the value of the product or article at certain time \(P\) and rate of depreciation \(r \%\), then we can find the depreciated value at \(n\) years that is:
 
Depreciated value at \(n\) years \(A\) =P(1r100)n.