The temperature, C, in degrees celsiud recorded by A city parks weather station between midnight and 7:00a.m. could be repredented ad A linear function of the number of hours after midnight, t, the temperature at 1:30a.m was -4.2°c and was -8.2°c at 7:00a.m which equation could be used to represent this fraction?
A: C(t)=-1.25t+-8.6
B: C(t)=-1.25t-4.2
C: C(t)=-0.8t-4.2
D: C(t)=-0.8t-3
Would it be a or b? It late and I've never done this before😔, I don't know what to do, but I think I got it down to a or b, but I don't know what is is. Please help!
C = at+b
Use the two data points and you have
1.5a + b = -4.2
7.0a + b = -8.2
5.5a = -4
a = -0.727
So b = -3.1
So I get C(t) = -0.7t - 3.1
I suspect a typo.
To determine the equation that could represent the temperature recorded by the city park's weather station, we need to determine the slope (rate of change) and the y-intercept.
Given that the temperature at 1:30 a.m. was -4.2°C and at 7:00 a.m. was -8.2°C, the change in temperature over this duration is (-8.2) - (-4.2) = -4°C.
The number of hours that elapsed from 1:30 a.m. to 7:00 a.m. is 5.5 hours (7 - 1.5 = 5.5).
To find the slope, we divide the change in temperature (-4°C) by the change in time (5.5 hours):
Slope (m) = (-4°C) / (5.5 hours) = -0.7273°C/hour (approximated to four decimal places).
Now we have the slope (-0.7273) and we need to find the y-intercept. By substituting the slope and one of the temperature values and the time value into the general linear equation C(t) = mt + b, we can solve for the y-intercept (b).
Using the temperature at 1:30 a.m. (-4.2°C) and the corresponding time of 1.5 hours:
-4.2 = (-0.7273)(1.5) + b
-4.2 = -1.0909 + b
b = -4.2 + 1.0909
b = -3.1091 (approximated)
Therefore, the linear equation that represents the temperature recorded by the city park's weather station is:
C(t) = -0.7273t - 3.1091.
The correct equation from the given options is:
D: C(t) = -0.8t - 3.