Question

The temperature of a weather station was 12.8 °F at midnight and fell 1.4 °F each hour for six hours. Which of the following solutions are viable for (h,T) where h is the number of hours after midnight and T is the temperature in degrees Fahrenheit?

Answer 1

Explanation:

The answer is (5, 5.8)

Answer 2

Let's try to find a linear relation like:

T(h) = a*h + b

where a is the slope and b is the y-intercept.

h is the number of hours after midnight.

T is the temperature at the time defined by h.

We know that at midnight, the temperature is 12.8°F.

At midnight, we have h = 0, then:

T(0) = a*0 + b = 12.8°F

b = 12.8°F

Now we know that our function is:

T(h) = a*h + 12.8°F

We also know that the temperature fell 1.4 °F each hour for six hours.

Then the slope will be -1.4°F

We can write the linear relationship as:

T(h) = -1.4°F*h + 12.8°F (for 0 ≤ h ≤ 6)

Where we have a restriction in the possible values of h, because we know that this model only works for six hours after midnight,