Exponential Growth & Decay Lesson 8.7

43210 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. 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.F-IF.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.

Growth: goes up in value, use this formula! y = c(1+r) t 1+r>1 Decay: goes down in value, use this formula! y = c(1- r) t 1- r <1

Example: You buy a new 10 speed bike for $150. It loses value at a rate of 15% per year. What is it’s worth in 3 years? Worth = cost(rate) years w = c(1-0.15) 3 (a loss means –15%) w = 150(.85) 3 w = The bike was only worth $92.12 in 3 years.

Identify the following as growth or decay  y = 500(1.20) 5  y = 375(.078) t  y = 5(1.078) 6  y = 30(.99) 4

Write a general equation for the following  You purchased a car for $35,000. The minute you drove it off the lot it started going down in value by 1.3%. Write an equation for its value in the future.  You just purchased a painting as an investment and it is suppose to appreciate it value at a rate of 3.65% each year. Write an equation for its value in the future. V = 35,000(0.987) t V = P(1.0365) t