Question

It is 76°f at the 6000-foot level of a mountain, and 49°f at the 12,000-foot level of the mountain. write a linear equation to find the temperature tt at an elevation xx on the mountain, where xx is the height in feet. enter answers as decimals rounded to the 4 digits.

Answer 1

`t(x) = 103 -0.0045x`

Explanation:

We are given the following in the question:

Let the equation:

`t(x) = a + bx`

be the linear equation that represent temperature at an elevation x.

Temperature at 6000-foot level = 76 f

`76 = a + 6000b`

Temperature at 12000-foot level = 49 f

`49 = a + 12000b`

Solving the two equation, we get,

`76-49 = -6000b\\27=-6000b\\\\b = (-27)/(6000)\\\\b = -0.0045\\76 = a + (-0.0045)6000\\76 = a -27\\a = 76 + 27\\a =103`

Thus, we can write the linear equation as:

`t(x) = 103 -0.0045x`