Answer:
Therefore, we have:
At (t) = 0 , D = - 6 sin 0 + 81 = 81
At (t) = 6 AM, D = - 6 sin ( π /2 ) + 81 = 79
t = 12 (noon), D = - 6 sin π + 81 = 81
t = 18 , (6:00 pm) , D = - 6 sin 3π / 2 + 81 = 79
Step-by-step explanation:
To start solving for this question, let us define or assume a Sine Function for easy solving.
Defining the given parameters, we have:
Temperature = 81 - 69 = 12
Recalling from the question that
Temperature = number of hours before midnight,
Therefore Temperature (T) = 6
Also, we know that the give period of time is 24 hrs
:
Therefore,
We have: 2π / k = 24
hours
Therefore,Making (K) the subject of formula, we have:
24 k = 2π
k = π / 12
Thus,
D = 6 sin ( π / 12 ) ( t ) + 81
With a given range of 81 and 69,
However, we know that the temperature after midnight would decrease, whereas our function has it increasing to 81 when t = 6 AM.
So therefore, we can attempt to swap the function, so we have:
D = -6 sin (π / 12 ) t + 81
Therefore, we have:
At (t) = 0 , D = - 6 sin 0 + 81 = 81
At (t) = 6 AM, D = - 6 sin ( π /2 ) + 81 = 79
t = 12 (noon), D = - 6 sin π + 81 = 81
t = 18 , (6:00 pm) , D = - 6 sin 3π / 2 + 81 = 79
I hope this helps.
