a. correct
b. put x=27, solve
c. put x=64, solve
(a) Find a function R giving the revenue per day realized from the charter.
R(x) = -4x^2+350x+8600
(b) What is the revenue per day if 47 people sign up for the cruise?
$ ?
(c) What is the revenue per day if 84 people sign up for the cruise?
$ ?
b. put x=27, solve
c. put x=64, solve
If "x" represents the number of passengers above 20, then the total number of passengers would be 20 + x.
For each additional passenger above 20, the fare is reduced by $4 per day. So the revenue per day for each additional passenger is $430 - $4x.
To find the total revenue per day, we multiply the number of passengers by the fare per person per day:
R(x) = (20 + x) * ($430 - $4x)
Expanding and simplifying the expression:
R(x) = 20 * $430 + 20 * (-$4x) + x * ($430 - $4x)
= $8600 - $80x + $430x - $4x^2
= - $4x^2 + $350x + $8600
Therefore, the function R giving the revenue per day realized from the charter is R(x) = -4x^2 + 350x + 8600.
(b) To find the revenue per day if 47 people sign up for the cruise, we substitute x = 47 - 20 = 27 into the function R(x):
R(27) = -4(27)^2 + 350(27) + 8600
= -4(729) + 9450 + 8600
= -2916 + 9450 + 8600
= 5134
So, the revenue per day if 47 people sign up for the cruise is $5134.
(c) To find the revenue per day if 84 people sign up for the cruise, we substitute x = 84 - 20 = 64 into the function R(x):
R(64) = -4(64)^2 + 350(64) + 8600
= -4(4096) + 22400 + 8600
= -16384 + 22400 + 8600
= 7456
So, the revenue per day if 84 people sign up for the cruise is $7456.