Chapter 4.1, Problem 6E

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

Unit Conversion with Exponential Growth The exponential function $N=3.93\times {1.34}^d$ gives the approximate U.S. population, in millions, $d\text{decades}$ after $1790$. (The formula is valid only up to $1860$.)

a. What is the yearly growth factor? Find a formula that gives the population $y\text{years}$ after $1790$.

b. What is the century growth factor? Find a formula that gives the U.S. population $c\text{centuries}$ after $1790$. (Assume that the original formula is valid over several centuries.)