According to the U.S. Bureau of the Census, the estimatedand projected midyear world
Chapter 2, Problem 13(choose chapter or problem)
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 \(t\) , 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 \(d N / d t\) there. Interpret your result as a rate of change.
(b) The instantaneous growth rate is defined as
\(\frac{d \mathrm{~N} / \mathrm{dt}}{\mathrm{N}}\)
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.
Equation Transcription:
Text Transcription:
N
t
N
t
t=2000
dN/dt
dN/dt /N
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