Problema Solution

Suppose the population of a country in 1985 was 145 million. In 1995 it was 190 million. Use the formula P = Ae kt to setup an expression to estimate the population of the country in 2005.

Answer provided by our tutors

For t = 0 years after 1985

P = 145 millions


P = Ae^(k*0)


A = 145


now the formula is P=145 e^(kt), we need to find k


For t = 10 years 1985 that is in the year of 1995

P = 190 millions


190 = 145* (e^(k*10))


190/145 = e^10k


10k = ln(190/145)


k = (1/10)ln(190/145) = 0.027029033


so, P = 145*e^(0.027029033t)


In the year of 2005 we have t = 2005 - 1985 = 20 years


P = 145* e^(0.0270290339*20)


P = 248.96 millions


the population in the year of 2005 will be 248.96 million.