# Differentiate between linear and exponential functions Focus 8

Differentiate between linear and exponential functions.

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. 4 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. 3 2 Students will construct, compare, and Students will interpret linear and exponential construct, compare, function models and solve problems and interpret linear in context with each model. function models and - Compare properties of 2 functions solve problems in in different ways (algebraically, context with the model. graphically, numerically in tables, - Describe a situation verbal descriptions) where one quantity - Describe whether a contextual changes at a constant situation has a linear pattern of rate per unit interval as change or an exponential pattern of compared to another. 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. 1 0 Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal.

§ Linear functions take the form y = mx + b. § An exponential function is in the form y = ax. § It is easy to see the difference between a linear and exponential function on a graph.

§ Linear functions change at a constant rate per unit interval. § An exponential function changes by a common ratio over equal intervals. x 2 x 1 2 2 4 3 6 3 8 4 16 5 10 5 32 6 12 6 64 7 128 8 16 8 256 9 18 9 512 10 20 10 1, 024

§ Sebastian deposits $100, 000 in a local bank that will pay out 5% interest every year. Is this example linear or exponential? § A certain type of corn grows at the rate of 3 inches per week. Is this example linear or exponential? § The Munn Sugar Processing Plant is able to process 10 tons of sugar per month. Assuming that this process stays steady, is this example linear or exponential? § Exercise biologist, Samantha, discovered that to reduce soreness, people should start biceps curls at 10 pounds. Then, progress weekly to 11 pounds, 14 pounds, 20 pounds, 32 pounds, 56 pounds and so on. Is this example linear or exponential?

- Slides: 5