Logarithmic Modeling Worksheet
This worksheet focuses on logarithmic modeling, including understanding logarithmic functions, solving equations, and applying them to real-world scenarios for Grade 11 students.
Includes
Standards
Topics
Logarithmic Modeling
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Date:
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following functions represents logarithmic decay?
y = log(2x)
y = log(0.5x)
y = 2^x
y = (1/2)^x
2. The Richter scale measures the magnitude of earthquakes using a logarithmic scale. An earthquake with a magnitude of 7 is how many times more intense than an earthquake with a magnitude of 5?
2 times
10 times
100 times
1000 times
3. The inverse of an exponential function is a function.
4. The domain of the function f(x) = log(x) is .
5. Explain how to determine the base of a logarithm from its graph.
6. Sketch the graph of y = log₂(x + 3) - 1. Identify the domain, range, and any asymptotes.
Domain:
Range:
Asymptote(s):
7. The population of a certain bacteria culture can be modeled by the equation P(t) = 100 * log(t + 2), where P(t) is the population after t hours. How long will it take for the population to reach 300?