Logarithm Word Problems
Practice solving real-world problems using logarithmic functions, including exponential growth and decay, pH calculations, and decibel measurements.
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Logarithm Word Problems
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Read each problem carefully and use your knowledge of logarithms to solve them. Show all your work.
1. A population of bacteria doubles every 3 hours. If there are initially 100 bacteria, how long will it take for the population to reach 10,000 bacteria?
2. The pH of a solution is given by the formula pH = -log[H+], where [H+] is the hydrogen ion concentration. A solution has a hydrogen ion concentration of 1.0 x 10^-5 mol/L. The pH of this solution is .
3. The loudness of a sound in decibels (dB) is given by D = 10 log(I/I₀), where I is the intensity of the sound and I₀ is the intensity of the softest audible sound. If a rock concert has a sound intensity 10^12 times greater than I₀, what is the decibel level of the concert?
4. If a substance decays by half every 10 years, then after 20 years, only 25% of the original substance remains.
True
False
5. You invest $5000 in an account that earns 7% interest compounded continuously. How long will it take for your investment to double?
6. The Richter scale measures the magnitude of an earthquake using the formula M = log(I/I₀), where I is the intensity of the earthquake and I₀ is the intensity of a standard earthquake. An earthquake measures 6.5 on the Richter scale. What is its intensity compared to the standard earthquake?
I = 6.5 I₀
I = 10^6.5 I₀
I = log(6.5) I₀
I = 6.5/I₀