The following table gives the percent of the US population living in urban areas

Question

The following table gives the percent of the US population living in urban areas as a function of year.3

Year 1800 1830 1860 1890 1920 Percent 6.0 9.0 19.8 35.1 51.2 Year 1950 1980 1990 2000 Percent 64.0 73.7 75.2 79.0
(a) Find the average rate of change of the percent of the population living in urban areas between 1830 and 1880 (round to 3 decimals) percent/yr

(b) Estimate the rate at which this percent is increasing at the year 1990. (percent/yr)
c) Estimate the rate of change of this function for the year 1830. (percent/yr)
(d) Is this function increasing or decreasing?

Explanation / Answer

a)pop. in 1830 = 9.0

pop. in 1890 = 35.1

change = 26.1

time = 60 years

Thus, rate of change = 26.1/60 = 0.435 per year

b)pop. at 1990 = 75.2

pop. at 2000 = 79.0

change = 3.8

time = 10 years

Thus, rate of change = 3.8/10 = 0.380 per year

c)pop. at 1830 = 9.0

pop. at 1860 = 19.8

change = 10.8

time = 10 years

Thus, rate of change = 1.08 per year

d) The function is an increasing function as the no. keeps on increasing for each subsequent year.

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