p(t)=100((1)/(2))^((t)/( 8.02)) Radioactive isotopes are unstable atoms that decay into other atoms. lodine-131 is a radioactive isotope. The function models p, the percentage of iodine-131 atoms remaining in a sample after t days. To the nearest tenth of a percent, what percent of iodine-131 atoms remain in the sample after 10 days? (Ignore the % symbol when entering your answer. For example, if the answer is 11.2%, enter 11.2 .)

Question

p(t)=100((1)/(2))^((t)/( 8.02)) Radioactive isotopes are unstable atoms that decay into other atoms. lodine-131 is a radioactive isotope. The function models  p, the percentage of iodine-131 atoms remaining in a sample after  t days. To the nearest tenth of a percent, what percent of iodine-131 atoms remain in the sample after 10 days? (Ignore the  % symbol when entering your answer. For example, if the answer is  11.2%, enter 11.2 .)

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Identify Function and Value: Identify the given function and the value of t for which we need to find p(t). The function given is p(t) = 100 * (1/2)^(t/8.02), which models the percentage of iodine-131 atoms remaining after t days. We need to find the percentage remaining after t = 10 days.Substitute Value into Function: Substitute the value of t into the function. We substitute t = 10 into the function to find p(10). p(10) = 100 * (1/2)^(10/8.02)Calculate Exponent: Calculate the exponent. We need to calculate (1/2)^(10/8.02). First, we calculate the fraction 10/8.02. 10/8.02 ≈ 1.247 Now we raise (1/2) to the power of 1.247. (1/2)^1.247Use Calculator for Calculation: Use a calculator to find the value of (1/2)^1.247. Using a calculator, we find that (1/2)^1.247 ≈ 0.435.Find Percentage by Multiplication: Multiply the result by 100 to find the percentage. Now we multiply the result from the previous step by 100 to find the percentage of iodine-131 remaining after 10 days. p(10) = 100 * 0.435 p(10) ≈ 43.5

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