Worksheet: Logarithmic Regression Model

In this worksheet, we will practice using the exponential regression features on a graphing calculator to model data exhibiting logarithmic growth or decay.

Q1:

We can model data with nonlinear regression.

Which scatterplot shows data that could be modeled by logarithmic regression?

  • A
  • B
  • C
  • D

Which formula models logarithmic regression?

  • A 𝑦 = 𝑎 + 𝑏 ( 𝑥 ) l n
  • B 𝑦 = 𝑎 𝑏 ( 𝑥 ) l n
  • C 𝑦 = 𝑎 + 𝑏 ( 𝑥 ) l n
  • D 𝑦 = 𝑎 𝑏 ( 𝑥 ) l n
  • E 𝑦 = 𝑎 + ( 𝑥 ) 𝑏 l n

Q2:

An app creator tracked the sales of his app for the first 14 days after it was released. Since the sales slowed over time, a logarithmic model can be used to model the data.

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Total Number of Sales since Launch 217 552 807 897 1 001 1 080 1 126 1 162 1 218 1 275 1 290 1 335 1 367 1 393

Use a calculator to calculate the regression equation 𝑦 = 𝑎 + 𝑏 ( 𝑥 ) l n . Round the values of 𝑎 and 𝑏 to 1 decimal place.

  • A 𝑦 = 3 3 1 . 7 + 2 9 7 . 3 ( 𝑥 ) l n
  • B 𝑦 = 4 3 4 . 5 + 2 6 9 . 6 ( 𝑥 ) l n
  • C 𝑦 = 2 9 7 . 3 + 3 3 1 . 7 ( 𝑥 ) l n
  • D 𝑦 = 2 6 9 . 6 + 4 3 4 . 5 ( 𝑥 ) l n

Predict the total number of sales after 4 weeks.

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