Answer:
(a) b = π/26
c = 4·π/13
(b) The amplitude = 55 million cans
he average value of the soup sales cycle = 160 million cans
Step-by-step explanation:
(a) The given information are;
The volume of the cans of condensed soup sold = 16-oz
The maximum number of cans sold = 215 million
The time at which the maximum number of cans are sold = The 5th week of the year
The minimum number of cans sold = 105 million
The time at which the minimum number of cans are sold = The 31st week of the year
The function representing the number of cans sold = Sine function
f(x) = a·sin(b·x + c) + d
The period, p = 2π/b
When bx + c = 0
x = -c/b
When bx + c = π/2
x = (π/2 - c)/b = 5
(π/2 - c)/5 = b
When bx + c = 3·π/2
x = (3·π/2 - c)/b = 31
(3·π/2 - c)·5/(π/2 - c) = 31
Solving, we get
c = 4·π/13
b = π/26
(b) The amplitude and average value of soup sales
The amplitude = a = The distance from the midpoint to the highest or lowest point of the function
∴ a = (215 - 105)/2 = 55 million cans
The average value of the soup sales cycle = d = The midline
d = 105 million + 55 million = 160 million cans.
