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.
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.