College Algebra, Exercise P, Exercise P.1, Section Exercise P.1, Problem 8

Suppose a mountain climber models the temperature $T (\text{in }^\circ F)$ at elevation $h(\text{in ft})$ by $T = 70-0.003 h$
a.) Find the temperature $T$ at an elevation of 1500 ft.

Given:
$h = 1500 \text{ft} - $ elevation
$T = 70 - 0.003 h$ model

So,

$
\begin{equation}
\begin{aligned}
T &= 70 - 0.003 (1500) && \text{Substitute } h = 1500\\
\\
T &= 70 - 4.5 && \text{Simplify}\\
\\
T &= 65.5 ^\circ F && \text{Temperature at an elevation of 1500 ft}
\end{aligned}
\end{equation}
$


b.) If the temperature is $64 ^\circ F$, what is the elevation?

Given:
$T = 64 ^\circ F -$ Temperature
$T = 70 - 0.003 h$ model

Solving $T = 70 - 0.003 h$ for $h$

$
\begin{equation}
\begin{aligned}
T - 70 &= 70 - 0.003 h - 70 && \text{Subtract both sides by } h\\
\\
\frac{T - 70}{-0.003} &= \frac{\cancel{-0.003}h}{\cancel{-0.003}} && \text{Divide both sides by -0.003}\\
\\
\frac{-70 - T}{0.003} &= h && \text{model}\\
\\
h &= \frac{70-64}{0.003} \text{ft} && \text{Substitute } T = 64 ^\circ F\\
\\
h &= 2000 \text{ft} && \text{Elevation if the temperation is } 64 \circ F
\end{aligned}
\end{equation}
$

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