A 9713e0004t describes the population A of a country in mill

A= 971.3e^0.004t describes the population, A, of a country in millions, t years after 2003. determine the year when the population of the country will be 1082 million

Solution

A = 971.3e^0.004t

A = 1082 million

==> 1082 = 971.3e^0.004t

==> e^0.004t = 1082/971.3

==> e^0.004t = 1.113971

Apply natural logarithms on both sides

==> ln e^0.004t = ln 1.113971

==> 0.004t lne = ln 1.113971          ; since ln a^b = b ln a

==> 0.004 t (1) = ln 1.113971

==> t = (1/0.004) ln 1.113971

==> t = 26.9827

==> t = 27

Hence the population will be 1082 million in 2030 (since t starts from 2003) (2003 + 27 = 2030)