Question
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 $f^{\prime}(t)$ and $f^{-1}(t)$ 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?(c) In what year was the population growing at the greatest rate?
Step 1
Since $t$ is the number of years after 1800, $t$ for the year 1925 would be $1925 - 1800 = 125$. Looking at the graph of $f(t)$, we find that $f(125)$ is approximately 125 million. So, the population in 1925 was approximately 125 million. Show more…
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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. $18(\mathrm{a})$. The graphs of $f^{\prime}(t)$ and $f^{\prime \prime}(t)$ are shown in Figs. $18(\mathrm{~b})$ and $18(\mathrm{c})$. (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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