Question

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8200 ​ft, the liquid boils at 199.42°F. At an altitude of 4700 ​ft, the liquid boils at 206.07°F. Write an equation giving the boiling point b of the​ liquid, in degrees​ Fahrenheit, in terms of altitude​ a, in feet. What is the boiling point of the liquid at 2500 ​ft?

Write an equation.
b=nothing

Answer 1

The boiling point of the liquid it 210.25°F

Explanation:

Linear Modeling

Some real-life events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to build the model and predict unknown behaviors.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

`\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

We are given the following points (H,A) where A is the altitude and P is the boiling point of a certain liquid: (8200,199.42) and (4700,206.07)

Applying the formula:

`\displaystyle B-199.42=(206.07-199.42)/(4700-8200)(A-8200)`

Calculating:

`\displaystyle B-199.42=(6.65)/(-3500)(A-8200)`

`\displaystyle B-199.42=-0.0019(A-8200)`

`\displaystyle B-199.42=-0.0019A+15.58`

`\displaystyle B=-0.0019A+15.58+199.42`

The equation is:

`\displaystyle B=-0.0019A+215`

Finally, we calculate the boiling point at A=2500 ft:

\displaystyle B=-0.0019*2500+215

B = 210.25°F

The boiling point of the liquid it 210.25°F