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|
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.