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A certain radioactive material decays at a continuous rate of 4% per year. If the initial mass is 195 grams, how much of the mass remains after 45 years?

You may use the formula A(t)=A where A(t)is measured in grams
The mass that remains after 45 years is ________ grams.
Round answer to 1 decimal place.

User Krsi
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Final answer:

The mass of the radioactive material remaining after 45 years, originally 195 grams decaying at 4% per year, is computed using an exponential decay formula and rounded to one decimal place, resulting in 32.2 grams.

Step-by-step explanation:

Radioactive Material Decay Calculation

The question involves determining the amount of a radioactive material that remains after a certain period, given its continuous rate of decay. The decay of radioactive materials is an exponential process and is described by decay equations. For a substance that decays at a continuous rate, the amount remaining can be calculated using the formula A(t) = A0e−rt, where A(t) is the amount of substance at time t, A0 is the initial amount, e is the base of natural logarithms, and r is the decay rate.

In this case, the radioactive material has an initial mass of 195 grams and it decays at a rate of 4% per year. To calculate the mass remaining after 45 years, we can substitute the given values into the decay equation:

A(45) = 195 * e−(0.04 * 45).

Performing this calculation:

  • A(45) = 195 * e−(1.8)
  • A(45) = 195 * 0.16529888822158656
  • A(45) = 32.23329717230636 grams

Therefore, after rounding to one decimal place, the mass remaining after 45 years is 32.2 grams.

User Badr Hari
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