Make sure you’re on Slide 6: Changing Scale (Exponential and Logarithmic) of Fitting Wealth-v-Health and Exploring Logarithmic Models.

Balancing Logarithmic Growth

  • The folder for a logarithmic function g is shown in red, and the folder for h is "turned off". Do not turn it on yet!

  • Both the x- and y-axis are be labeled with a sequence of numbers (e.g. 0, 2, 4, 6 …​).

1 What kind of growth do the sequences on these axes show? (circle one) Linear Quadratic Exponential Logarithmic

2 The function g is Linear, Quadratic, Exponential, or Logarithmic, and its base is . Which two points are plotted on g?

  • Click on the wrench button () in the top-right corner of the Desmos graph to open the "Graph Settings" window.

3 The x-axis goes from ≤ x ≤ . Can you change these numbers to make g look linear? Why?

  • Click on the wrench button () and change the x-axis from Linear to Logarithmic

4 Did our two points on the line change? How did the graph change?

5 What is going on here?

6 Make a prediction: What would the graph of g look like with a Linear x-axis a Logarithmic y-axis?

7 Try it out! Was your prediction accurate? . What happened, and why?

Balancing Exponential Growth

  • Set the scale for both axes back to Linear.

  • "Turn off" the folder for g, and "turn on" the folder for our exponential function h.

8 The function h is Linear, Quadratic, Exponential, or Logarithmic, and its base is . Which two points are plotted on h?

9 Without switching either axis to Logarithmic, can we change the minimum and maximum x or y to make h look Linear?

10 Make a prediction: Which axis should we switch to Logarithmic, in order to make h look Linear?

11 Try it out! Was your prediction accurate? . What happened, and why?

  • Change the y-axis back to Linear, and change the x-axis to Logarithmic

12 What happened to the graph of h, and why?

★ Desmos has two choices for scale:

  • Linear (each interval is the same size as the one before it)

  • Logarithmic (each interval is 10x larger than the one before it)

If we wanted to make h appear linear using the x-axis, what kind of scale would we need?

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