Given:
In 1999, the number of mosquitos = 2500
They tripled every year.
To find:
The model for this situation and find the number of mosquitos in 2005.
Solution:
The general exponential modal is
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and 0<b<1 is decay factor and b>1 is growth factor.
In 1999, the number of mosquitos is 2500.
Initial value: [tex]a=2500[/tex]
They tripled every year. So, growth factor is 3>1 and it is exponential growth.
Growth factor: [tex]b=3[/tex]
Putting [tex]a=2500[/tex] and [tex]b=3[/tex] in (i), we get
[tex]y=2500(3)^x[/tex] ...(ii)
Here, y is the population of mosquitos after x year of 1999.
Therefore, the required exponential growth modal is [tex]y=2500(3)^x[/tex].
We know that,
[tex]2005-1999=6[/tex]
Putting x=6 in (ii), we get
[tex]y=2500(3)^6[/tex]
[tex]y=2500(729)[/tex]
[tex]y=1822500[/tex]
Therefore, the estimated number of mosquitos in 2005 is 1822500.
