Chapter 2, Problem 13RE

According to the U.S. Bureau of the Census, the estimated and projected midyear world population, $N$ , in billions for the years $1950,1975,2000,2025$ , and $2050$ was $2.555,4.088,6.080,7.841$ , and $9.104$ , respectively. Although the increase in population is not a continuous function of the time $r$ , we can apply the ideas in this section if we are willing to approximate the graph of $N$ versus $t$ by a continuous curve, as shown in the accompanying figure.

(a) Use the tangent line at $t=2000$ shown in the figure to approximate the value of $dN\text{/}dt$ there. Interpret your result as a rate of change.

(b) The instantaneous growth rate is defined as

$\frac{dN/dt}{N}$

Use your answer to part (a) to approximate the instantaneous growth rate at the start of the year $2000$ . Express the result as a percentage and include the proper units.