Question

This is exponential growth and decay

Answer 1

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

$y=ab^x$          ...(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: $a=2500$

They tripled every year. So, growth factor is 3>1 and it is exponential growth.

Growth factor: $b=3$

Putting $a=2500$ and $b=3$ in (i), we get

$y=2500(3)^x$           ...(ii)

Here, y is the population of mosquitos after x year of 1999.

Therefore, the required exponential growth modal is $y=2500(3)^x$.

We know that,

$2005-1999=6$

Putting x=6 in (ii), we get

$y=2500(3)^6$

$y=2500(729)$

$y=1822500$

Therefore, the estimated number of mosquitos in 2005 is 1822500.