# A biologist studying a population of geckos for several years found that the population can be modeled as where P is the population, and t is in the time in years.  P= 230( 1.04)^t . What is the growth rate of this population?

Feb 28, 2017

Annual growth is 4 %.

#### Explanation:

Take your growth equation and plug some numbers in: $P = 230 {\left(1.04\right)}^{t}$

• $t = 0 , P = 230 {\left(1.04\right)}^{0} = 230$

• $t = 1 , P = 230 {\left(1.04\right)}^{1} = 230 \left(1.04\right)$

• $t = 2 , P = 230 {\left(1.04\right)}^{1} = 230 {\left(1.04\right)}^{2}$

You should see that there annual growth is by a factor of $1.04 \equiv 104 \text{%}$

So annual growth is 4 %.