## Related questions with answers

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

Verifieda.) 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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