The population (in millions) of the United States (excluding Alaska and Hawaii) t years after 1800 is given by the function f(t) in Fig. 18(a). The graphs of f′(t) and f″(t) are shown in Figs. 18(b) and 18(c).

(a) What was the population in 1925?

(b) Approximately when was the population 25 million?

(c) How fast was the population growing in 1950?

(d) When during the last 50 years was the population growing at the rate of 1.8 million people per year?

(e) In what year was the population growing at the greatest rate?

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250 200 150 100 50 y 0 (1800) 50 y = f(t) 100 150 Y 2 1 0 (1800) 50 y = f'(t) 100 150 .01 0 -.01 (a) (b) Figure 18 (a) Population (in millions) of the United States from 1800 to 1998. y=f"(t) 50 100 140 (c)