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Interpreting Rate of Change on a Ratio Scale
A researcher is plotting the price of a new technology over several years. In the first year, the price dropped from $10,000 to $5,000. Ten years later, the price dropped from $100 to $50 over a one-year period. If this data were plotted on a graph with a ratio (logarithmic) scale for the vertical price axis and a standard linear scale for the horizontal time axis, how would the steepness of the line segment representing the first year's drop compare to the steepness of the line segment representing the drop ten years later? Explain your reasoning.
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Choosing the Appropriate Scale for Data Visualization
A graph displays a company's revenue over a 10-year period. The vertical axis uses a ratio scale where each major gridline represents a doubling of revenue (e.g., $1M, $2M, $4M, $8M). The horizontal axis is a standard linear scale representing years. If the data points for the company's revenue form a straight, upward-sloping line on this graph, what can be concluded about the company's revenue growth?
Interpreting Rate of Change on a Ratio Scale
Analyzing Growth Rates with Appropriate Chart Scales
An analyst is tracking the market adoption of a new technology. The data shows that the number of users is doubling approximately every six months. The analyst wants to create a chart that most clearly illustrates whether this constant rate of growth is being maintained over several years. Which of the following chart configurations would be the most effective for this specific purpose?
A graph plots the cost per unit for two different technologies, A and B, over a ten-year period. The vertical axis uses a ratio scale, where each major gridline represents a halving of the cost (e.g., $100, $50, $25). Both technologies are represented by straight, downward-sloping lines, but the line for Technology A is steeper than the line for Technology B. What can be concluded by comparing the two lines?
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Interpreting Data on Different Scales
An analyst is creating charts to visualize different data trends over time. The charts all use a standard linear scale for the horizontal (time) axis, but a ratio (logarithmic) scale for the vertical axis. Match each described data trend with how it would appear as a line on this specific type of chart.
Interpreting Rate of Change on a Ratio Scale