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# 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.

 x 2x 2x Interval for 2x Interval for 2x 1 2 2 2 4 4 2 2 3 6 8 2 4 4 8 16 2 8 5 10 32 2 16 6 12 64 2 32 7 14 128 2 64 8 16 256 2 128 9 18 512 2 256 10 20 1024 2 512

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.