### 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 $$A$$ $=\phantom{\rule{0.147em}{0ex}}P\phantom{\rule{0.147em}{0ex}}{\left(1+\frac{r}{100}\right)}^{n}$
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 $$A =$$ $P\left(1+\frac{{r}_{1}}{100}\right)\left(1+\frac{{r}_{2}}{100}\right)\left(1+\frac{{r}_{3}}{100}\right).......\left(1+\frac{{r}_{n}}{100}\right)$.
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 $A\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}P\phantom{\rule{0.147em}{0ex}}{\left(1-\frac{r}{100}\right)}^{n}\phantom{\rule{0.147em}{0ex}}$.
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 $$A$$ $=P\phantom{\rule{0.147em}{0ex}}{\left(1-\frac{r}{100}\right)}^{n}\phantom{\rule{0.147em}{0ex}}$.