Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
8.2 Negative and Zero Exponents I love exponents! Focus 8 Learning Goal – (HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.FIF.C.8 & 9, and HS.F-LE.A.1) = Students will construct, compare and interpret linear and exponential function models and solve problems in context with each model. 4 3 2 1 0 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model. - Compare properties of 2 functions in different ways (algebraically, graphically, numerically in tables, verbal descriptions) - Describe whether a contextual situation has a linear pattern of change or an exponential pattern of change. Write an equation to model it. - Prove that linear functions change at the same rate over time. - Prove that exponential functions change by equal factors over time. - Describe growth or decay situations. - Use properties of exponents to simplify expressions. Students will construct, compare, and interpret linear function models and solve problems in context with the model. - Describe a situation where one quantity changes at a constant rate per unit interval as compared to another. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Definition of Negative Exponents (let a be a nonzero number and let n be a positive integer) The expression a-n is the reciprocal of an . n 1 = a a-n = 1 a≠0 a-n an 3-2 = 1 32 =1 9 The negative exponent says the number needs to be moved to the opposite location and made positive. If it’s negative in the numerator, it belongs in the denominator position positive. If it’s negative in the denominator position, it belongs in the numerator position positive. Definition of Zero Exponent (let a be a nonzero number and let n be a positive integer) A nonzero number to the zero power is ALWAYS 1! a0 = 1 a 0 30 = 1 (x2y5)0 = 1 The expression 00 is undefined. Simplify expressions: write with positive exponents. (-5)-3 = 1 = -1 (-5)3 125 244-3 = 24 ∙ 1 = 24∙ 1 = 3 43 -3-4 = 1 = - 1 4 -3 81 64 8 Simplify expressions: write with positive exponents. 3a-3b-2 = 33 2 ab (3-3)2 = 3(-3 ∙ 2) = 3-6 = 1 1 = 6 3 729 Graphing with a variable as an exponent Sketch the graph of y = 2x x 3 2 1 0 -1 -2 -3 2x 8 4 2 20=1 2-1= ½ 2-2 = ¼ 2-3 = 1/8 Will it ever touch the x-axis? Example: (Just follow this example to see what you get to do on your assignment.) Between 1970 and 1990, the Missouri population increased at a rate of .47% per year. The population P in t years is given by: P = 4,903,000 1.0047t Where t = 0 for 1980 Find the population in 1970, 1980, and 1990 To find the population, plug the numbers into the formula and then use a calculator. Pop in 1970 t = -10 Pop in 1990 t = 10 Do you expect it to be more or less in 1970 than 1980? P = 4,903,000 1.0047-10 (set up the problem) = 4,678,406 (calculate) This is the population in 1970. Population in 1990: P = 4,903,000 1.004710 P = 5,138,376