2.14

Logarithmic Function Context and Data Modeling

about 30 min · 6 short parts · stop after any part
Some real data grows fast at first, then slows down: learning words, cooling coffee, prices.
By the end you can spot that pattern, fit a log model on your calculator, and use it to predict.

The path

  1. 1
    Warm-up: undoing ln and log
    You can solve 5+2ln⁡x=135 + 2\ln x = 13.
  2. 2
    Spot log data in a table
    You can tell log data from linear and exponential, and say why.
  3. 3
    Fit a model with LnReg
    You can get y=a+bln⁡xy = a + b\ln x from data on a calculator.
  4. 4
    Use the model
    You can predict yy from xx, and find xx from yy.
  5. 5
    Formula problems
    You can use N=N0ertN = N_0e^{rt}, decibels and cooling formulas both ways.
  6. 6
    AP mix: tables and rational functions
    You can read f−1f^{-1} from a table, compose, and check zeros and end behavior.