Answer:
A = 175, B = π/6, C = 345
Step-by-step explanation:
The given variation of the volume in the tank and time includes are;
At t = 0 the volume in the tank, y = Maximum volume, [tex]y_{max}[/tex] = 520 gallons
At t = 6 the volume in the tank, y = Minimum volume, [tex]y_{min}[/tex] = 170 gallons
The function that models the situation is y = A·cos(B·x) + C
Given that the function that models the situation is the cosine function, we have;
A = The amplitude = (The maximum - The minimum)/2
∴ A = (520 - 170)/2 = 175
A = 175
The period = The time to change from maximum to minimum = 2 × The time to change from maximum (t = 0) to minimum (t = 6)
∴ The period = 2 × (6 - 0) = 12
The period = 12 seconds = 2·π/B
∴ B = 2·π/12 = π/6
B = π/6
C = The vertical shift = Th minimum + A = (The maximum + The minimum)/2
∴ C = (520 + 170)/2 = 345
C = 345
