Word Problems/price-wise function
Assume you work at a company where you are paid hourly. You are paid $7.80 per hour for regular time (less than or equal to thirty-five hours) and time and three-quarters for overtime hours up to forty-five hours in one week. If you are asked to work forty-five or more hours in one week you are paid double-overtime. Write this information in the form of a piecewise-defined function and be sure to include the domain for each piece. Also, check your model by calculating the pay for working thirty-five hours and for working thirty-six hours. Post these values as well.
Let x=the number of hrs worked per week, and w(x)=weekly pay (in $'s)...
for 0<=x<=35, w(x)=7.80x
for 35<x<45, w(x)=7.80*35+7.80(1+3/4)(x-35)=13.65x-204.75
for x>=45, w(x)7.80*35+7.80(1+3/4)*10+7.80*2(x-45)=15.6x-292.5
x=35 ==> w(35)=7.80*35=273
x=36 ==> w(36)=13.65*36+-204.75=286.62
x=46 ==> w(46)=15.6*46-292.5=425.10
I hope this helps.