Question

The population p (in millions) of Italy from 1990 through 2008 can be approximated by the model p=56.8e^o.oo15t , where t represents the year with t=0 corresponding to 1990
-Find the populations of Italy in 2000 and 2008
-Use the model to predict the populations of Italy in 2015 and 2020

Answer 1

As we already have the model that describes the change of the population in Italy in terms of the years that have elapsed, we only have to replace the conditions that are requested in that equation.

Therefore to find the population of Italy in the year 2000 (t = 10 years)  substitute t = 10 in the equation and have:

$p = 56.8e^{0.0015*10}$

$p=57.6584$ million people

To find the population of Italy in 2008 (t = 18 years)

substitute t = 18 in the equation and have:

$p=56.8e ^{0.0015*18}$

$p=58.3545$ million people

To predict the population in Italy for 2015 and 2020 with this model, we substitute in the equation t = 25 and t = 30

t = 25

$p=56.8e^{0.0015*25}$

$p=58.9704$ million people

 t = 30

$p=56.8e^{0.0015*30}$

$p=59.4144$ million people