Exercise 1.4.28

Question

The table gives the population of the United States, in millions, for the years 1900 –2010. Use a graphing calculator (or computer) with exponential regression capability to model the US population since 1900 . Use the model to estimate the population in 1925 and to predict the population in the year 2020 .

\begin{figure}[ht]\centering
\begin{tabular}{|c|c|}
\hline Year & Population \
\hline 1900 & 76 \
1910 & 92 \
1920 & 106 \
1930 & 123 \
1940 & 131 \
1950 & 150 \
1960 & 179 \
1970 & 203 \
1980 & 227 \
1990 & 250 \
2000 & 281 \
2010 & 310 \
\hline
\end{tabular}
\end{figure}

Khagan Gulusoy · Accepted Answer

WolframAlpha models the function of time $t$ as follows:

$$
\forall t \in[1900, \infty): \quad f(t)=8.627 	imes 10^{-9} e^{0.012103034 t} 	ext {. }
$$

For $t=1925$, we have:

$$
f(1925)=8.6278 \cdot 10^{-9} e^{0.0121034 \cdot 1925} \approx 113.383 .
$$

for $t=2020$, we have:

$$
f(2020)=358.021 .
$$

(the population in USA in 2020 was actually $\approx 329.5 \mathrm{mln}$.)

Exercise 1.4.28

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Year	Population

1900	76
1910	92
1920	106
1930	123
1940	131
1950	150
1960	179
1970	203
1980	227
1990	250
2000	281
2010	310

Exercise 1.4.28

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