LINEAR VS. EXPONENTIAL GROWTHDifferentiate between linear and exponential functions.

4 3 2 1 0In 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.

WHAT IS THE DIFFERENCE BETWEEN LINEAR AND EXPONENTIAL FUNCTIONS?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.

WHAT IS THE DIFFERENCE BETWEEN LINEAR AND EXPONENTIAL FUNCTIONS?Linear functions change at a constant rate per unit interval.

An exponential function changes by a common ratio over equal intervals.

x 2x

1 2

2 4

3 6

4 8

5 10

6 12

7 14

8 16

9 18

10 20

x 2x

1 2

2 4

3 8

4 16

5 32

6 64

7 128

8 256

9 512

10 1,024

IS THE EXAMPLE LINEAR OR EXPONENTIAL? 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?