SOLUTION: This question deals with the half-life formula. Use the approximate half-life formula in this exercise. Be sure to discuss whether the formula is valid for the case described.

Click here to see ALL problems on Exponents

Question 112150: This question deals with the half-life formula. Use the approximate half-life formula in this exercise. Be sure to discuss whether the formula is valid for the case described.
32. A clean-up project is reducing the concenration of a pollutant in the water supply with an 8% decrease per week. What is the half-life of the concentration of the pollutant? What fraction of the original amount of the pollutant will remain when the project ends after 1 year (52 weeks)?
This is the approximate half-life formula: For a quantity decaying exponentially at a rate of P% per time period, the half-life is approximately Thalf = approximately 70/P. This approximation works best for small decay rates and breaks down for decay rates about 15%.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A clean-up project is reducing the concenration of a pollutant in the water supply with an 8% decrease per week. What is the half-life of the concentration of the pollutant? What fraction of the original amount of the pollutant will remain when the project ends after 1 year (52 weeks)?
---------------------------
This is the approximate half-life formula: For a quantity decaying exponentially at a rate of P% per time period, the half-life is approximately T(half) = approximately 70/P. This approximation works best for small decay rates and breaks down for decay rates about 15%.
---------------------------
T(half) = 70/8 = 8.75 per week
T(half) = 8.75*52 = 455 per year
------------------------------
Comment: This all seems rather strange but that's the
result using the formula.
Cheers,
Stan H.