Question

A webmaster makes $24 an hour for the first 38 hours she works during a
week and $31 an hour for each hour worked over 38 hours. Which piecewise
equation models her total weekly pay y in dollars as it relates to the number
of hours x that she has worked during the week?
24x
O A. e=1
OSXS38
x > 38
(31x+912
0 [24x
O B. y = {31(x – 38) +912 x > 38
S24x
(31x
C. y =
OSXS 38
X> 38
(24x
OSX 38
D. y = {31(x-38)
x > 38

Answer 1

A piecewise function is consists of different relationships between the variables over different intervals

The correct piecewise equation that models her total weekly pay is option B.

$\mathbf{B.} \ y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}$

The given parameters are;

The amount made by the webmaster for the first 38 hours she works = $24

The amount she makes for each hour worked after the first 38 hours = $31 an hour

Required:

To find the piecewise equation that models the total weekly pay, y, in dollars in relation to the number of hours x that she has worked during the week

Solution:

If she works for x ≤ 38 hours

The amount she makes working x less than or equal to 38 hours, y = $24/hour × x hours = $24 × x hours

The total amount the webmaster wakes by working all through the normal 38 hours is $24/hour × 38 hours = $912

If she works over 38 hours, (x > 38) we have;

The number of hours she works over 38 hours = x - 38

The amount she makes each hour after working 38 hours, y = $31/hour × (x - 38) hours

The total amount she makes y working for more than 38 hours is given as follows;

y = 31·(x - 38) + 912

The piecewise equation that models her weekly pay is therefore, presented as follow;

$y = \begin{cases} 24 \cdot x& \ 0 \leq x \leq 38 \\ 31\cdot (x - 38) + 912 & \ x > 38 \end{cases}$

The above piecewise function is the same as option B

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