Question

For a private lesson, rate, R, depends on the number of hours, h. If a student takes 6 or fewer hours, they pay at flat fee of $100 and $160 per hour. If a student takes more than six hours, they pay a flat fee of $800 for the first six hours and an additional $160 for each additional credit.
What is the rate for 8 hours of lesson?
b) (3 pts)'Express the tuition functions R(h) as a piecewise function with two pieces. Each piece should be a linear function.
c) (3 pts) If the rate is $1880, how many hours of lessons were taken?
d) (2 pts) Please use plain language to interpret the vertical intercept and slope?

Answer 1

Answer:

a) $1120

b) R(h)= [ 160h + 100 for h< or = to 6 hours

             [160h + 800 for h > 6 hours

C) 12.75 hours

d) as the number of hours increases the rate also increases.

Step-by-step explanation:

Given: for a lesson less than or equal to 6 hours flat rate fee $100 and per hour charge $160

          For a lesson greater than 6 hours flat rate fee is $800 and the per extra credit charge is    

          $160.

a) For a 8 hour lesson we know 6 hours cost a flat fee charge of $800 plus $160 *2 hours that are extra on the 6 hours which will be $320 then add up the $800( 6 hour rate)+ $320 ( the two hour rate above 6 hours to add to 8 hours) is equal to $1120.

b) For a linear function we take the first portion of the statement that for a lesson less than or equal to 6 hours the flat rate fee is $100 an=d per hour charge is $160 so the first piece of the linear equation is R(h)= 160h + 100 using the format of y= mx + c where $100 is the constant c which is a flat rate fee, then m= 160 as this is a dependant variable on the number of hours which are less than 6. Condition is h<= 6

The second equation is R (h) = 160h+ 800 which we were given a flat fee of $800

        Then $160 is the dependant variable which depends on hours after each additional      credit. Condition h>6 as given on the statement.

So the piecewise function is R (h) = [160h + 100 for h <= 6

                                                                [160h + 800   for h>6

c) we know that for 8 hours the rate is $1120 therefore for a rate of $1880 the hours are above 6 so we use the second linear function for h>6.

R (h) = $1880

Therefore $1880=160h + $800 then we solve for h

1880-800 = 160h

1080= 160h

1080/160=h

6.75 hours = h  

Then we add 6 hours because the rate is in the second function.

Therefore the number of hours taken for a rate of $1880 is 12.75 hours.

d) As the number of hours increases the rate also increases. The y intercept represents the rate and the slope is represented by the $160 that varies with the number of hours taken.

Answer 2

Answer:

(a) $1120 (c) 12.75hrs

Step-by-step explanation: see attachment