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Common Core Standards: Math

High School: Functions

Linear, Quadratic, and Exponential Models F-LE.1b

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Likewise, show this numerically, so students can see that as x increases by 1, the interval between the two equations is constant for one function, but not the other.

x2x2xInterval for 2xInterval for 2x
122
24422
36824
481628
51032216
61264232
714128264
8162562128
9185122256
102010242512

As we can see, the linear function increases by a difference of 2 every time. The interval for the exponential function, however, has a much larger difference with every interval (each difference increases by a factor of 2 every time). That's the difference.

Aligned Resources

    More standards from High School: Functions - Linear, Quadratic, and Exponential Models

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