Logarithmic Modeling Worksheet
This worksheet focuses on logarithmic modeling, including understanding logarithmic functions, converting between forms, and solving real-world problems.
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Standards
Logarithmic Modeling
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. The of a number is the exponent to which another fixed value, the base, must be raised to produce that number.
2. The equation y = log_b(x) is equivalent to the exponential equation .
3. The domain of a logarithmic function f(x) = log_b(x) is all real numbers.
4. Which of the following is equivalent to log₂(16) = 4?
4² = 16
16² = 4
2⁴ = 16
log₄(16) = 2
5. Convert the exponential equation 5³ = 125 into its equivalent logarithmic form.
6. The population of a certain bacteria doubles every hour. If the initial population is 100 bacteria, how long will it take for the population to reach 1000 bacteria? Use the formula P(t) = P₀ * 2^(t/d), where P(t) is the population at time t, P₀ is the initial population, and d is the doubling time.
7. The graph of y = log(x) has a vertical asymptote at x = 0.
True
False
8. Sketch the graph of y = log₂(x). Identify the x-intercept and the domain.