# The population of Detroit, Michigan was 951,300 in 2000. Detroit has been experiencing a population decline of 1.4% per year since 2000. What is the projected population for 2005 in Detroit?

Mar 3, 2016

$886 , 548$

#### Explanation:

The formula that describes this population's variation is given by:
$P = {P}_{o} \cdot {\left(1 - i\right)}^{\Delta t}$
Where
${P}_{0}$ is the population in a referencial time (${t}_{0}$)
$P$ is the population in a time $t$ around ${t}_{0}$
$i$ is the rate of fhe population growth
$\Delta t = t - {t}_{0}$ is the difference between a time of interest and the referencial time

In the problem
${P}_{0} = 951 , 300$
i=-1.4%=-0.014
$\Delta t = 2005 - 2000 = 5$

So

$P = 951.300 \cdot {\left(1 - 0.014\right)}^{5} = 951 , 300 \cdot 0 , {986}^{5} = 886 , 548$