High School: Functions
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.