Chapter 2.5, Problem 68E

World population growth. From the dawn of humanity to $1830$, world population grew to one billion people. In $100$ more years (by $1930$ ) it grew to two billion, and $3$ billion more were added in only $60$ years (by $1990$ ). In $2016$, the estimated world population was $7.4$ billion with a relative growth rate of $1.13\%$.

(A) Write an equation that models the world population growth, letting $2016$ be year $0$.

(B) Based on the model, what is the expected world population (to the nearest hundred million) in $2025$ ? In $2033$ ?