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 + ( 𝑥 ) 𝑏 l n
  • C 𝑦 = 𝑎 𝑏 ( 𝑥 ) l n
  • D 𝑦 = 𝑎 + 𝑏 ( 𝑥 ) l n
  • E 𝑦 = 𝑎 𝑏 ( 𝑥 ) 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)ln. Round the values of 𝑎 and 𝑏 to 1 decimal place.

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

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?

  • A 𝑛 against 𝑡
  • B 𝑛 against 𝑡
  • C l o g 𝑛 against 𝑡
  • D 𝑛 against 𝑡
  • E 𝑛 against log𝑡

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