A sample of radium has a weight of 1.5 mg

Annalise Rogers

Annalise Rogers

Answered question

2022-02-10

A sample of radium has a weight of 1.5 mg in a half-life of approximately 6 years. a) how much of the sample will remain after 6 years? 3 years? 1 year? b) find a function F which models the amount of radium f(t), in mg, remaining after t years​

Answer & Explanation

limegreenleosp9

limegreenleosp9

Beginner2022-02-11Added 12 answers

Given: 
The original amount of radium is 
A0=1.5 mg. 
The given half-life period is 
t12=6 years. 
a) The expression for the radium after the given time is, 
A=A02t12 
In the formula above, replace t and the specified numbers with 6 instead.
A=1.5 mg266 
=1.5 mg2 
=0.75 mg 
In the formula above, replace t and the specified values with 3 instead.
A=1.5 mg236 
=1.5 mg2 
=1.060 mg 
In the formula above, replace t and the specified values with 1 instead.
A=1.5 mg216 
=1.336 mg 
Thus, the amount of radium after 6 years is 0.75 mg, the amount of radium after 3 years is 1.060 mg, and the amount of radium after 1 year is 1.336 mg. 
b) The expression for the radium after the given time is, 
f(t)=A02t12 
Substitute 6 for t12, and 1.5 for A0 in the above expression. 
f(t)=A02t6 
Thus, the function that represents the amount of radium left after t time is f(t)=A02t6

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