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MAT 095 – LAB 2 – Exponents, Order of Operations Please show your work! All your answers need to be justified to receive credit! Evaluate and rewrite(with tutor): 2 6= (−3) 4 = (−6) 3 = − 42 = 10 2 = 10 3 = 10 6 = Simplify the following expression. 1. (−7) 2 2. 2 3 + (−3) 2 3. (−6) 2 − (−2) 3 4. (−4) ⋅ 108 5. 3 ⋅ 10 3 − 9 3 6. 103 × 10 6 7. 100,000,000 ÷ 10 4 Sample Problem and Solution(with tutor): Anastasia notices that for every tomato she picks off her plants on one day, there are three tomatoes a week later. One Monday, a single tomato appears on one of her plants. If Anastasia keeps picking the tomatoes as they appear, how many tomatoes will the on the plant the first following Monday? The second following Monday? There was one tomato, which she picked Monday. So a week later (the following Monday) there are 3 tomatoes. After she picks the three tomatoes, each one of them gives 3 more tomatoes. So the second Monday there will be 3 x 3 = 9 tomatoes. Write a mathematical expression for how many tomatoes will be on the plant the tenth following Monday (indicate how you reached this mathematical expression): Each of the tomatoes she picks gives 3 tomatoes a week later, so we see that the pattern is “each week we multiply by 3”: First following Monday 3 tomatoes, Second following Monday 3 x 3 = 32 tomatoes Third following Monday 3 x 3 x 3 = 33 tomatoes… so on the tenth following Monday the plant will have 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3= 310 tomatoes. QUESTIONS 8 – 12 REFER TO THE FOLLOWING: The first mobile telephone call, in the 1940s, didn’t exactly correspond to our current idea of cell-phone calls—it used over 80 pounds’ worth of electronic equipment! Researcher Martin Cooper of Motorola is credited with making the first call on a handheld (if rather heavy) handset on April 3, 1973—to his rival Dr. Joel S. Engel at Bell Labs. Since the race between Motorola and Bell to develop the first portable mobile phone, cell-phones have enjoyed ever-growing popularity*. (Sample question) Suppose that annual cell-phone sales double each year. Suppose further that a single cell phone was sold in 1973. How many were sold in 1974? Solution: Since only one cell phone was sold in 1973 and we supposed that the annual cell-phone sales would be doubled afterward, two cell phones were sold in 1974 because 2( the increase of the sales amount in one year(1974-1973)) ×1(the actual amount of sales in 1973) = 2 × 1 = 2 8) How many were sold in 1975? 9) How many were sold in 1976? 10) How many were sold in 1977 11)[extra points] Can you anticipate the sales of cell phone in 1983 in this sales model? Write (and evaluate) the mathematical operations to justify your reasoning: 12)[extra points]Write a mathematical operation using exponents (DO NOT EVALUATE) to describe how many cell phones were sold in the year 2003. Explain your reasoning!