in the formula Nlekt n is the number of items in terms of an

in the formula N=le^(kt), n is the number of items in terms of an initial population, l, at a given time, t, and k is a growth per unit. how long will it take for the population of a certain country to double if it\'s annual growth rate is 6.1%? (please show steps and how you got last step. (I\'ve gotten it down to 2=e^(6.1)t.

Solution

N = I e^kt

growth rate k = 6.1% = 0.061

Double the initial population ==> N = 2I

==> 2I = I e^0.061t

==> e^0.061t = 2

Apply natural logarithms on both sides

==> ln e^0.061t = ln 2

==> 0.061t (ln e) = ln 2         since ln a^b = b ln a

==> 0.061t = ln 2         since ln e= 1

==> t = (1/0.061) ln 2          (ln 2 = 0.693

==> t = 11.36

Hence it would take 11.36 years for the population to double