Q6. - Algebra 1

Question

the highest point in North Carolina is Mt. Mitchell at an elevation of 2,037 meters above sea level. Suppose the position of a hiker is given by the function $\mathit{p}\mathbf{\left(}\mathbf{t}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{5}\mathit{t}\mathbf{+}\mathbf{2037}$, where $\mathit{t}$ is the number of minutes. Which of the following is the best interpretation of the slope of the function?

$\mathit{F}$ The hiker’s initial position was 2307 feet below sea level.

$\mathit{G}$ The hiker’s initial position was 2037 feet above sea level.

$\mathit{H}$ The hiker is descending at a rate of $\mathbf{2}\mathbf{.}\mathbf{5}$ meters per minute.

$\mathit{J}$ The hiker is ascending at a rate of $\mathbf{2}\mathbf{.}\mathbf{5}$ meters per minute.

Step-by-Step Solution

Answer

The hiker is descending at a rate of $\mathbf{2}\mathbf{.}\mathbf{5}$ meters per minute. 

Step 1. Plot the graph.

Plot the given function, $p\left(t\right)=-2.5t+2037$.

Step 2. Observation.

From the graph it can be observed that the slope of the function has negative sign, therefore, it is descending with the time.

Step 3. Write the conclusion.

From the given equation, it can be observed that the hiker is descending at a rate of $2.5$

meters per minute.

Therefore, option $H$ is the required answer.