To find the revenue per day for a specific number of passengers, we can use the function R(x) = -4x^2 + 350x + 8600.
(a) The function R(x) represents the revenue per day realized from the charter. In this case, x represents the number of passengers above 20.
(b) To find the revenue per day if 47 people sign up for the cruise, we need to calculate R(47).
R(47) = -4(47)^2 + 350(47) + 8600
= -4(2209) + 16450 + 8600
= -8836 + 16450 + 8600
= 9314 + 8600
= $17,914
Therefore, the revenue per day if 47 people sign up for the cruise is $17,914.
(c) Similarly, to find the revenue per day if 84 people sign up for the cruise, we need to calculate R(84).
R(84) = -4(84)^2 + 350(84) + 8600
= -4(7056) + 29400 + 8600
= -28,224 + 29400 + 8600
= -28,224 + 38,000
= $9,776
Therefore, the revenue per day if 84 people sign up for the cruise is $9,776.