Chapter 4.1, Problem 12E

Reminder Round all answers to two decimal places unless otherwise indicated.

Long-Term Population Growth Although exponential growth can often be used to model population growth accurately for some periods of time, there are inevitably, in the long term, limiting factors that make purely exponential models inaccurate. From 1790 to 1860, the U.S. population could be modeled by $N=3.93\times {1.03}^t\text{million}$ people, where $t$ is the time in years since 1790. If this exponential growth rate had continued until today, what would be the population of the United States have been in 2015? Compare your answer with the actual population of the United States in 2015, which was about $323\text{million}$.