Logarithm Word Problems Worksheet
Solve real-world problems using logarithms, including growth, decay, and Richter scale applications.
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Logarithm Word Problems
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Read each word problem carefully and use your knowledge of logarithms to solve them. Show all your work.
1. The population of a certain city is growing at an annual rate of 3%. If the current population is 250,000, how many years will it take for the population to reach 400,000? Use the formula P = P₀(1 + r)ᵗ.
2. If you invest $5,000 at an annual interest rate of 6% compounded continuously, how long will it take for your investment to double? Use the formula A = Pe^(rt). The time required is approximately years.
3. 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. What is the half-life of this substance?
10 years
13.86 years
20 years
50 years
4. The magnitude M of an earthquake is measured on the Richter scale, which is given by M = log₁₀(I/I₀), where I is the intensity of the earthquake and I₀ is the intensity of a standard earthquake. If an earthquake has an intensity 10,000 times I₀, what is its magnitude?
5. A sound that is 100 times more intense than another sound is 20 decibels louder. (The decibel level D is given by D = 10 log₁₀(I/I₀)).
True
False