Exercise 1.4.23

Question

Suppose the graphs of $f(x)=x^{2}$ and $g(x)=2^{x}$ are drawn on a coordinate grid where the unit of measurement is 1 inch. Show that at a distance $2 \mathrm{ft}$ to the right of the origin, the height of the graph of $f$ is $48 \mathrm{ft}$ but the height of the graph of $g$ is about $265 \mathrm{mi}$.

Khagan Gulusoy · Accepted Answer

For $x=2\mathrm{~ft}=24$ inches, we have:

$$
f(x)=24^{2}=576 \mathrm{in}=48 \mathrm{~ft} ; \quad g(x)=2^{24}=16777216 	ext { in }\approx 264.79191919 \mathrm{mi} \approx 265 \mathrm{mi} 	ext {, }
$$

as desired. $\Box$

Exercise 1.4.23

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Exercise 1.4.23

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