AP® Precalculus – Semi-log Plots – Drill 20

About This Drill

AP® Precalculus – Semi-log Plots – Drill 20 is a Math practice drill covering Semi-log Plots. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

This AP(r) Precalculus drill focuses on semi-log plots (Topic 2.15): interpreting graphs where one axis uses a logarithmic scale, recognizing that a straight line on a semi-log plot signals an exponential relationship, and converting between semi-log linear equations and explicit exponential functions.

Questions in This Drill

1. A semi-log plot shows a straight line with the vertical axis representing \( \log_{10} y \). The line passes through \( (0, 1) \) and \( (2, 3) \). Which of the following exponential functions best models the data?
2. A researcher plots data on a semi-log graph with time \( t \) in years on the horizontal axis and \( \log_{10}(P) \) on the vertical axis, where \( P \) is a population. The plotted points appear to lie on a straight line. Which of the following conclusions is best supported?
3. The table below shows values of \( t \) and \( \log_{10}(N) \) for a bacterial culture.

   t	log10(N)
   0	2.0
   1	2.3
   2	2.6
   3	2.9
   4	3.2

   Which of the following best describes the relationship between \( N \) and \( t \)?
4. A semi-log plot of experimental data produces the linear equation \( \log_{10} y = 0.5x + 2 \). Which of the following is an equivalent equation for \( y \) in terms of \( x \)?
5. A semi-log plot shows \( \log_2(P) \) on the vertical axis and time \( t \) on the horizontal axis. The graph is a straight line passing through \( (0, 2) \) and \( (4, 4) \). What is the doubling time of \( P \) -- the length of time required for \( P \) to double?