Question

bismouth - 210
bismuth - 210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining bismuth - 210 transforms into another atom (polonium - 210 in this case) each day. if you begin with 205 mg of bismuth - 210, how much remains after 7 days?
after 7 days, mg of bismouth - 210 remains.
round your answer to the nearest hundredth as needed.
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Explanation:

Step1: Write the exponential decay formula

The formula for exponential decay is \(A = A_0(1 - r)^t\), where \(A_0\) is the initial amount, \(r\) is the decay rate, and \(t\) is the time. Here, \(A_0=205\) mg, \(r = 0.13\), and \(t = 7\).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate \((0.87)^7\)

\((0.87)^7\approx0.3773\) (using a calculator)

Step4: Calculate the final amount \(A\)

\(A = 205\times0.3773\approx77.35\)

Answer:

\(77.35\)