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write and solve an equation to determine how long it will take for the temperature to reach -1 degrees Fahrenheit.the temperature at 1 pm is 35 degrees Fahrenheit. the temperature changes -4 degrees Fahrenheit per hour.

User Gertie
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1 Answer

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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

User Yuan
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