In a simplified model for taxes, a person will pay: 10% on the first $40,000 earned; 20% on the next $50,000 earned; 40% on the rest. For instance, a person earning $30,000 will pay $3,000 in taxes, and a person earning $100,000 will pay 10% x 40,000+ 20% x 50, 000 + 40% x 10,000 = 18,000 dollars in taxes. 1. If a person has an income of x 0, write down the function T describing the amount of money that they pay for taxes. Explain and simplify the formulas as much as possible. Do not use the % sign! 2. 2. Write down the function M1 describing the net income of a person (income minus taxes) as a function of their gross income x. Explain and simplify the formulas as much as possible. 3. Draw the graph of M1 for x between 0 and 120, 000. You can do it by hand or copy from a graphing calculator. 4. A common misconception about taxes is that earning more money can make you fall into another tax bracket, and you will then earn less money. Explain why this is wrong. Your answer should be "We see that the function M1 is ..., which means...".