Many income tax systems are calculated using a tiered method. under certain tax law, the first $100 000 of earning are subject to a 35% tax, earnings greater than $100 000 and up to $500 000 are subjects to a 45% tax. any earnings greater than $500 000 are taxed at 55%. write a piecewise function that models this situation.

Talia took the bus from her home to the bank and then walked back to her home along the same route. the bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. to determine the time, x, that it took talia to walk home, she used the equation 40(0.9 – x) = 5x. the time of trip 2 is hours. the distance of trip 1 is km.