The linear plot of the exponential growth functions with the same 𝑟 value but different 𝑆0 values shows that the function with the larger 𝑆0 value is growing faster.However, the plot on the logarithmic scale for the y-axis (log plot) of the exponential growth functions with the same 𝑟 value but different 𝑆0 values appears to show both functions growing at the same speed, as the two functions are represented by parallel straight lines.Why does the log plot in fact show the function with the larger 𝑆0 value to be growing faster? Select the most appropriate answer.Group of answer choicesEach interval between ticks on a log scale represents an order of magnitude change in the value of the function, so an interval further up the y-axis represents a greater change in the value of the function than an interval lower down the y-axis.Each tick on a log scale represents an additive change in the value of the function, whereas each tick on a linear scale represents a multiplicative ('fold') change in the value of the function.A increasing function with a larger initial value will always grow faster than an increasing function with a smaller initial value.A log scale uniformly compresses the y-axis, so a function that starts higher up the y-axis will be growing faster than one that starts lower down the y-axis.
Question
The linear plot of the exponential growth functions with the same 𝑟 value but different 𝑆0 values shows that the function with the larger 𝑆0 value is growing faster.However, the plot on the logarithmic scale for the y-axis (log plot) of the exponential growth functions with the same 𝑟 value but different 𝑆0 values appears to show both functions growing at the same speed, as the two functions are represented by parallel straight lines.Why does the log plot in fact show the function with the larger 𝑆0 value to be growing faster? Select the most appropriate answer.Group of answer choicesEach interval between ticks on a log scale represents an order of magnitude change in the value of the function, so an interval further up the y-axis represents a greater change in the value of the function than an interval lower down the y-axis.Each tick on a log scale represents an additive change in the value of the function, whereas each tick on a linear scale represents a multiplicative ('fold') change in the value of the function.A increasing function with a larger initial value will always grow faster than an increasing function with a smaller initial value.A log scale uniformly compresses the y-axis, so a function that starts higher up the y-axis will be growing faster than one that starts lower down the y-axis.
Solution
The most appropriate answer is: Each interval between ticks on a log scale represents an order of magnitude change in the value of the function, so an interval further up the y-axis represents a greater change in the value of the function than an interval lower down the y-axis.
This is because a logarithmic scale is a nonlinear scale used when there is a large range of quantities. In a logarithmic scale, each tick mark is a multiple of the previous one, unlike a linear scale where the difference between each tick mark is constant. Therefore, even though the lines appear parallel on a log plot, the function with the larger S0 value is growing faster because each interval on the y-axis represents a larger absolute change in the function's value.
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