Derive the formula for the population in Example 3, if the population in 1995 was 2 million.

Example 3

In 2005, people in a country suffering from economic problems started to emigrate to other countries. Let P(t) denote the population of the country in millions t years after 2005. Sociologists studying this population determined that for the next 30 years the number of people emigrating would gradually increase as the news of better prospects outside the country spread. Suppose that the rate of emigration is given by .004e^0.04t + .04 millions per year t years after 2005. Suppose further that the growth constant of the population is 3/125. Find a differential equation satisfied by P(t).