Question

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

Answer 1

Answer:

The function for the temperature is:

$T(t) = 2.4t - 2$

Step-by-step 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:

$T(t) = at - 2$

$10 = a*(5) - 2$

$5a = 12$

$a = \frac{12}{5}$

$a = 2.4$

So, the function for the Temperature is:

$T(t) = 2.4t - 2$