The owner of a luxury motor yacht that sails among the 4000 greek islands charges $540 per person per day if exactly 20 people sign up for the cruise. however, if more than 20 people (up to the maximum capacity of 90) sign up for the cruise, then each fare is reduced by $7 per day for each additional passenger. assume at least 20 people sign up for the cruise, and let x denote the number of passengers above 20.
(a) find a function r giving the revenue per day realized from the charter.
r(x) =
(b) what is the revenue per day if 48 people sign up for the cruise?
$
(c) what is the revenue per day if 78 people sign up for the cruise?
$

Step-by-step explanation:

Charges up to 20 passengers = $540 per person per day

Total charges = 540 × 20 = $10800

If x passengers above 20 sign up for the cruise then total number of passengers = (20 + x)

Total revenue = $(20+x)

But each fare is reduced by $7 for additional passenger above 20 then revenue generated R(x) = 540(20+x) - 7x

R(x) = 10800 + 540x - 7x

R(x) = 10800 + 533x

a). Revenue per day realized R = 10800 + 533x

b). R(48) = 10800 + 48×533

              = $36,384

C). R(78) = 10800 + 78×543

              = $53,154

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

-6 is the correct option from the above given options