Question

At higher elevations water boils at lower temperatures. The temperature at which water boils is

called the boiling point of water. At sea level the boiling point of water is 100°C, while at 2
kilometers of elevation (about 6550 feet) the boiling point of water is 94°C. The function that gives
the boiling point of water in °C, B, at an elevation of a kilometers is B(x) = 100 – 3.5.2,
Determine the elevations at which the boiling point of water is between 89 °C and 93 °C. Give your
answer accurate to 1 decimal place.The boiling point of water is between 89 °C and 93 °C when the elevation is between km and km.

Answer 1

The boiling point of water is between 89 °C and 93 °C at elevations ranging from approximately 2.0 km to 3.1 km. This is calculated using the function B(x) = 100 – 3.5x and by setting up inequalities.

Step-by-step explanation:

The given function for the boiling point of water in degrees Celsius (°C), B, at an elevation of x kilometers is B(x) = 100 – 3.5x. To determine the elevations at which the boiling point is between 89 °C and 93 °C, we set up two inequalities:

89 ≤ 100 – 3.5x (1)
93 ≤ 100 – 3.5x (2)

Solving inequality (1) for x gives us the minimum elevation where the boiling point is 89 °C:

89 ≤ 100 – 3.5x
3.5x ≤ 100 – 89
3.5x ≤ 11
x ≥ 11 / 3.5
x ≥ 3.14

Solving inequality (2) for x gives us the maximum elevation where the boiling point is 93 °C:

93 ≤ 100 – 3.5x
3.5x ≤ 100 – 93
3.5x ≤ 7
x ≥ 7 / 3.5
x ≥ 2

The elevations where water boils between 89 °C and 93 °C range from approximately 2.0 km to 3.1 km.