Question

X The temperature, C, in degrees Celsius recorded by a city park's weather station between midnight and 7:00 a.m. could be represented as a linear function of the number of hours after midnight, t. The temperature at 1:30 a.m. was – 4.2°C and was -8.6°C at 7:00 a.m. Which equation could be used to represent this function? (1 point) O C (t) = -0.8t – 4.2 OC (t) = -1.25t - 8.6 OC (t) = -0.8t - 3 OC (t) = -1.25t - 4.2​

Answer 1

C(t) = -0.8t - 3

Explanation:

We are told that the temperature at 1:30 a.m. was – 4.2°C and was -8.6°C at 7:00 a.m.

Thus, difference in temperature is;

ΔT = -8.6°C - (-4.2°C)

ΔT = -8.6°C + 4.2°C

ΔT = -4.4°C

Now, number of hours between 1:30 a.m and 7:00 a.m is 5.5 hours.

Thus, average temperature per hour is;

-4.4/5.5 = -0.8°C/h

Now, since C is represented as a linear function of the number of hours after midnight, t.

Then the linear function is -0.8t + x = C(t)

Let's find x.

After 1.5 hours, we have -4.2°C. Thus;

-0.8t + x = -4.2

-0.8(1.5) + x = - 4.2

-1.2 + x = -4.2

x = -4.2 + 1.2

x = -3

Thus, the linear relationship is now;

C(t) = -0.8t - 3