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Question

# On a particular day, the linear function defined by$f(x)=-3.52 x+58.6$approximates the temperature in degrees Fahrenheit above the surface of Earth, where x is in thousands of feet and y is the temperature. (Source: Schwartz, Richard H., Mathematics and Global Survival, Ginn Press.)(a) When the height is 5000 feet, what is the temperature? Solve analytically.(b) When the temperature is $-15^{\circ} \mathrm{F}$, what is the height? Solve analytically.(c) Explain how the answers in parts (a) and (b) can be supported graphically.

Solution

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a.) For this part, we simply plug in the given height into the given function. We must also take note of the units, so $x=5$. So now we would have:

\begin{aligned} f(5)&=-3.52(5)+58.6\\ &=-17.6+58.6\\ &=41^{\circ}F \end{aligned}

The temperature is about $41^{\circ}F$.

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