SOLUTION: 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 da

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Question 1208600: 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 215 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.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
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 215 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.
~~~~~~~~~~~~~~~~~~~~ 

The remaining mass of the Bismuth-210 after 1 day is  215*(1-0.13) = 215*0.87 mg.


The remaining mass of the Bismuth-210 after 2 days is  215*0.87*0.87 = 215*0.87^2 mg.


The remaining mass of the Bismuth-210 after 3 days is  215*0.87^2*0.87 = 215*0.87^3 mg.


. . . . . and so on . . . . . 


The remaining mass of the Bismuth-210 after 7 days is  215*0.87^6*0.87 = 215*0.87^7  = 81.10978 mg  (rounded).    ANSWER

Solved, with explanations.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 81.11 mg

Work Shown
P = 215 mg is the starting amount
r = 0.13 is the decimal form of the decay rate
t = 7 days
A = P*(1-r)^t ............... exponential decay equation
A = 215*(1-0.13)^7
A = 81.109780898733
A = 81.11 mg

The 210 is never used since it's part of the name, rather than an amount.
Some teachers love to place red herrings to distract students.
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