AP®︎ Precalculus: Topic 2.15 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 2.15 of AP Precalculus – Semi-log Plots.
Questions List
Topic 2.15
Question 1 Easy
A data point is plotted on a semi-log plot whose y-axis is logarithmically scaled with base 10 and labeled with output values. The marks labeled 1 and 10 are one vertical unit apart. How many vertical units above the mark labeled 1 is the point plotted?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 2.15: Semi-log Plots
Learning Objective: 2.15.A
Determine if an exponential model is appropriate by examining a semi-log plot of a data set.
Essential Knowledge: 2.15.A.1
In a semi-log plot, one of the axes is logarithmically scaled with logarithm base , where . When the -axis of a semi-log plot is logarithmically scaled, data or functions that demonstrate exponential characteristics will appear linear.
Essential Knowledge: 2.15.A.2
If for large input values of a bivariate data set the logarithms of the output values trend linear, then transformations of an exponential function can be used to model the data set. Therefore, an advantage of semi-log plots is that the dependent variable values do not need to be transformed by a constant to reveal that transformations of an exponential function would produce an appropriate model.
Learning Objective: 2.15.B
Construct the linearization of exponential data.
Essential Knowledge: 2.15.B.1
Techniques used to model linear functions can be applied to a semi-log graph.
Essential Knowledge: 2.15.B.2
For an exponential model of the form , the corresponding linear model for the semi-log plot is , where and . Specifically, the linear rate of change is , and the initial linear value is .
