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.