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Shtirlitz [24]
3 years ago
6

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

Mathematics
1 answer:
dybincka [34]3 years ago
4 0

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

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