Chapter 3.1, Problem 47E

World population. A mathematical model for world population growth over short intervals is given by

  $P=P_0{e}^{rt}$

where

  $\begin{array}{lll}{P}_0\hfill & =\hfill & \text{population}\text{at}\text{time}t = 0\hfill \\ r\hfill & =\hfill & \text{continuous}\text{compound}\text{rate}\text{of}\text{growth}\hfill \\ t\hfill & =\hfill & \text{time}\text{in}\text{years}\hfill \\ P\hfill & =\hfill & \text{population}\text{at}\text{time}t\hfill \end{array}$

How long will it take the world population to double if it continues to grow at its current continuous compound rate of 1.13% per year?