# Common Core Standards: Math

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#### The Standards

# 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 | 2^{x} | Interval for 2x | Interval for 2^{x} |

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.