Question

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 278 mg of bismuth - 210, how much remains after 7 days? after 7 days, mg of bismuth - 210 remains. round your answer to the nearest hundredth as needed. question help: video message instructor submit question jump to answer

Explanation:

Step1: Identify decay formula

The formula for exponential decay is $A = A_0(1 - r)^t$, where $A_0$ is the initial amount, $r$ is the rate of decay, and $t$ is the time.

Step2: Determine values

Here, $A_0=278$ mg, $r = 0.13$, and $t = 7$.

Step3: Substitute values into formula

$A=278\times(1 - 0.13)^7=278\times(0.87)^7$.

Step4: Calculate $(0.87)^7$

$(0.87)^7\approx0.377149$.

Step5: Calculate $A$

$A = 278\times0.377149\approx104.85$.

Answer:

$104.85$