Logarithmic Modeling Worksheet

Grade 12 Math worksheet on logarithmic modeling, covering applications, transformations, and interpretations of logarithmic functions.

Grade 12 Math LogarithmsLogarithmic Modeling

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Includes

3 Short AnswerMultiple ChoiceFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.B.3CCSS.MATH.CONTENT.HSF.LE.A.4

Topics

LogarithmsModelingFunctionsGrade 12 Math

8 sections · Free to use · Printable

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Logarithmic Modeling

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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. The population of a certain bacteria doubles every 3 hours. If the initial population is 100, write a logarithmic equation to model the time (t) it takes for the population to reach a certain number (P).

2. Which of the following graphs best represents a logarithmic function of the form y = log(x-h) + k?

Graph A (Increasing, passes through (1,0))

Graph B (Decreasing, passes through (1,0))

Graph C (Increasing, vertical asymptote at x=0)

Graph D (Decreasing, vertical asymptote at x=0)

3. The Richter scale for measuring earthquake intensity is a scale, meaning each whole number increase represents a tenfold increase in amplitude.

4. The formula for calculating the pH of a solution is pH = -log[H+], where [H+] is the concentration in moles per liter.

5. A radioactive substance decays according to the formula A = A₀e^(-0.05t), where A is the amount remaining after t years, and A₀ is the initial amount. How long will it take for half of the substance to decay? (Hint: Use logarithms to solve for t)

6. The domain of a logarithmic function y = log(x) is all real numbers.

True

False

7. Describe a real-world scenario where a logarithmic model would be more appropriate than a linear or exponential model to represent a given phenomenon.