Linear Modeling
When a variable changes at a constant rate, we use a linear model to write an equation to represent its behavior and make predictions.
Suppose we let:
t = time after 1 pm in hours
T = Temperature in degrees Fahrenheit
The equation of a line can be written as:
T = mt + b
Where m is the slope and b is the intercept.
We are given two data:
At 1 pm (t = 0) the temperature is 35. substituting in the equation.
35 = 0 + b
So the intercept is b = 35.
We also have the rate of change of the temperature per hour. That is the slope m = -4.
Now our model is complete:
T = -4t + 35
It's required to know when the temperature will reach T = -1 °F. Substituting:
-1 = -4t + 35
Subtracting 35:
-4t = -36
Dividing by -4:
t = -36 / (-4)
t = 9
This means that 9 hours from 1 pm the temperature will reach -1 °F