Logarithmic Modeling Worksheet

Logarithmic Modeling

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?

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.

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.