Given:
In 2010, the population of a town = 2000
Every year, it increase by 1.5%
To find the equation P(t) which represents the population of this town t years from 2010.
Formula
If a be the original population of a town and it increases by b% every year, after t year the population will be
[tex]a (1+\frac{b}{100} )^{t}[/tex]
Now,
Taking, a =2000, b = 1.5 we get,
[tex]P(t) = 2000(1+\frac{1.5}{100} )^{t}[/tex]
or, [tex]P(t) = 2000(1+0.015)^{t}[/tex]
Hence,
The population of this town t years from 2010 P(t) = [tex]2000(1+0.015)^{t}[/tex], Option D.
