# Chapter 1 - Section 1.4 - Exponential Functions - 1.4 Exercises - Page 54: 25

$f(24)=576 in$, which equates to 48 feet $g(24)=16777216 in$, which equates to 265 miles.

#### Work Step by Step

We are asked to find the height of two graphs using a given scale of 1 inch per coordinate box. We are asked to find the height at a distance of 2 feet from the origin, which would equate to 24 inches. Therefore, we must evaluate the functions at $x=24$. We are told that $f(x)=x^2$ and that $g(x)=2^x$ $$f(24)=576$$ $$g(24)=16777216$$ Using a conversion factor of 12 inches=1 foot, we can surmise that the height of $f(x)$ at $x=24$ is 48 feet, as we are told to prove in the beginning. Using a conversion factor of 63360 inches=1 mile, we can surmise that the height of $g(x)$ at $x=24$ is 265 miles, as we are asked to prove in the problem. Thus, we have shown the heights of each respective graph.

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