Question

At 8 a.m. the temperature was -2f at 1 pm the temperature was 12f warmer.

Create an addition equation that models the situation that models the situation and solve it to determine the new temperature.
Create your own number line to show how you found your solution.

Answer 1

The function for the temperature is:

`T(t) = 2.4t - 2`

Explanation:

This problem can be modeled by a first order equation in the following format:

`T(t) = at + b`

Using what the problem stated, we can build a system to mode the temperature.

Building the function:

The problem states that at 8 a.m. the temperature was -2f. To make the solution easier, I am going to say that 8 a.m. is the zero hour. So
`T(0) = -2`. It means that when
`t = 0, T(t) = -2`. With this, we can find the value of b in the function to determine the temperature.

`T(t) = at + b`

`-2 = a*(0) + b`

`b = -2`

Now we have that

`T(t) = at - 2`

The problem also states that at 1 pm the temperature was 12f warmer. 12f warmer is -2+12 = 10f. 1 p.m. is five hours from 8 a.m., so
`T(5) = 10`. We can substitute in the equation to find the value of a:

`T(t) = at - 2`

`10 = a*(5) - 2`

`5a = 12`

`a = (12)/(5)`

`a = 2.4`

So, the function for the Temperature is:

`T(t) = 2.4t - 2`