Chapter 3.1, Problem 50E

Population growth. Some developed nations have population doubling times of 200 years. At what continuous compound rate is the population growing? (Use the population growth model in Problem 47.)

47. 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?