Question

You have 500 micrograms of a certain radioactive material. in the course of each year 10 percent of the material decays. use the formula P()=P0 and round your answers to the nearest hundredth. after one year you have functionsequation editor micrograms of the material. after two years you have functionsequation editor micrograms of the material. after 10 years you have functionsequation editor micrograms of the material.

Answer 1

The amount of radioactive material remaining after a set amount of time can be calculated using an exponential decay formula. After one year 450 micrograms remain, after two years 405 micrograms, and after ten years approximately 348.68 micrograms of the initial 500 micrograms will be left.

Step-by-step explanation:

To calculate the amount of a certain radioactive material remaining after some time when a fixed percentage decays each year, we can use the decay equation which in this case follows a simple exponential decay function. Given that 10 percent decays each year, we can represent this with the equation P(t) = P0 (1 - 0.1)^t, where P(t) is the amount remaining after t years, and P0 is the initial amount of material.

So, starting with 500 micrograms:

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• After one year: P(1) = 500 (1 - 0.1)^1 = 500 * 0.9 = 450 micrograms
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• After two years: P(2) = 500 (1 - 0.1)^2 = 500 * 0.81 = 405 micrograms
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• After ten years: P(10) = 500 (1 - 0.1)^10 = 500 * (0.9)^10 ≈ 348.68 micrograms (rounded to the nearest hundredth)

The amount of radioactive material decreases exponentially as a function of time, and each quantity we've calculated is rounded to the nearest hundredth of a microgram to match the precision requested in the question.