the temperature (in degrees celsius) as a function of time (in hours since noon) for a certain day in san…

the temperature (in degrees celsius) as a function of time (in hours since noon) for a certain day in san jose, costa rica, is graphed. what is the approximate average rate at which the temperature decreases between 3:30 pm and 8:30 pm? choose 1 answer. 0.4 degrees celsius per hour 0.8 degrees celsius per hour 1.2 degrees celsius per hour 1.6 degrees celsius per hour

the temperature (in degrees celsius) as a function of time (in hours since noon) for a certain day in san jose, costa rica, is graphed. what is the approximate average rate at which the temperature decreases between 3:30 pm and 8:30 pm? choose 1 answer. 0.4 degrees celsius per hour 0.8 degrees celsius per hour 1.2 degrees celsius per hour 1.6 degrees celsius per hour

Answer

Explanation:

Step1: Determine the time values

3:30 pm is (3.5) hours since noon and 8:30 pm is (8.5) hours since noon. The change in time (\Delta t=8.5 - 3.5=5) hours.

Step2: Estimate the temperature values

From the graph, at (t = 3.5) (3:30 pm), (T(3.5)\approx24) degrees Celsius. At (t = 8.5) (8:30 pm), (T(8.5)\approx18) degrees Celsius. The change in temperature (\Delta T=18 - 24=- 6) degrees Celsius.

Step3: Calculate the average rate of change

The formula for the average rate of change of a function (y = f(x)) is (\frac{\Delta y}{\Delta x}). Here, for the function (T(t)) (temperature as a function of time), the average rate of change is (\frac{\Delta T}{\Delta t}). Substitute (\Delta T=-6) and (\Delta t = 5) into the formula: (\frac{\Delta T}{\Delta t}=\frac{-6}{5}=-1.2) degrees Celsius per hour. The magnitude (since we are asked about the rate at which it decreases) is (1.2) degrees Celsius per hour.

Answer:

C. (1.2) degrees Celsius per hour