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DakotaOliver
DakotaOliver
03.11.2021 • 
Mathematics

You are a volcanologist studying a recently active volcano. You need to get as close to the volcano as possible, but the temperature rises the closer you get, and your instruments will only function properly if the temperature is below 105°. In order to get accurate information about the area, you need to be within 500 feet from the base of the volcano. You have taken the following preliminary measurements: 5200 feet away the air temperature is 77°
4100 feet away the air temperature is 82°
3200 feet away the air temperature is 87°
2300 feet away the air temperature is 93°
1900 feet away the air temperature is 97°

If we use Temperature as the independent variable and Distance is the dependent variable, the equation y = -165x+17700, models the Distance (in feet) you are from the volcano as a function of the air temperature (in degrees Fahrenheit). Use this equation to answer the following questions.

a - What label would you put on the x-axis of a graph, distance or temperature? Why?
b - What label would you put on the y-axis? Why?
c - What is the domain and range of the situation? Why?
d - Predict the distance from the volcano when the air temperature is 100 degrees.
e - Predict the air temperature when you are 1000 feet from the volcano.
f - Given this information, would you guess the temperature will be too hot to do your research when you are within 500 ft of the volcano

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