Question

Zane is a dangerous fellow who likes to go rock climbing in active volcanoes. One time, when he was 202020 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He managed to climb up 444 meters each second and get out of the volcano safely. Graph Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds).

Answer 1

Answer:

f(x) = -4x + 20   

Refer attachment for graph.

Step-by-step explanation:

Given: when Zane was 20 meters below the edge of a volcano. He heard some rumbling, so he decided to climb up out of there as quickly as he could. He managed to climb up 4 meters each second and get out of the volcano safely.

We have to graph Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds).

Let he takes x seconds to get out of the volcano.

and y be the distance covered by the volcano to reach Zane.

Then, to reach the edge of volcano,  

Thus, The equation that represent Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds). is given by

f(x) = -4x + 20     

At x = 0 the Zane will be at f(0) = 20 that is 20 meter below the volcano.

Thus points are (0,20)

and when x = 5 Zane will be escaped from volcano.

Thus points are (5,0)

Plot this and obtained the graph for the given equation as attached below.

 

Answer 2

Answer:  The graph is attached below.

Step-by-step explanation: Given that when Zane was 20 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could.

He managed to climb up 4 meters each second and get out of the volcano safely.

We are to graph Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds).

Let, 't' represents the time (along X-axis) and f(t) represents Zane's elevation relative to the edge of the volcano(along Y-axis).

When t = 0, then f(t) = 20.

When t = 1, then f(t) = 20 - 4 = 16.

So, (0, 20) and (1, 16) are two points on the graph.

The slope of the line joining (0, 20) and (1, 16) is

$m=\dfrac{16-20}{1-0}=-4.$

Therefore, the equation of the line will be

$y-16=-4(x-1)\\\\\Rightarrow y-16=-4x+4\\\\\Rightarrow 4x+y=20.$

The graph of Zane's elevation relative to the edge of the volcano (in meters) as a function of time (in seconds) is shown in the attached figure.