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?

  • A𝑦=𝑎+𝑏(𝑥)ln
  • B𝑦=𝑎+(𝑥)𝑏ln
  • C𝑦=𝑎𝑏(𝑥)ln
  • D𝑦=𝑎+𝑏(𝑥)ln
  • E𝑦=𝑎𝑏(𝑥)ln

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.

Day1234567891011121314
Total Number of Sales since Launch2175528078971,0011,0801,1261,1621,2181,2751,2901,3351,3671,393

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

  • A𝑦=269.6+434.5(𝑥)ln
  • B𝑦=297.3+331.7(𝑥)ln
  • C𝑦=434.5+269.6(𝑥)ln
  • D𝑦=331.7+297.3(𝑥)ln

Predict the total number of sales after 4 weeks.

Q3:

Sophia suspects that the number of people, 𝑛, who have heard a rumour is an exponential function of the time 𝑡 since the rumour started. If she is correct, which of the following would give a straight line graph when plotted?

  • A𝑛 against 𝑡
  • B𝑛 against 𝑡
  • Clog𝑛 against 𝑡
  • D𝑛 against 𝑡
  • E𝑛 against log𝑡

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