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  • 23-07-2021
  • Mathematics
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Determine how many days t will the two isotopes have the same activity

Determine how many days t will the two isotopes have the same activity class=

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  • 23-07-2021

Answer:

t = 1 ... one day

Step-by-step explanation:

3 x [tex]10^{18}[/tex] * [tex](.5)^{t}[/tex] = 6 x [tex]10^{18}[/tex] * [tex](.5)^{2t}[/tex]

3 x [tex]10^{18}[/tex]     =   [tex](.5)^{2t}[/tex] / [tex](.5)^{t}[/tex]  

6 x [tex]10^{18}[/tex]      

1/2 = [tex].5^{t}[/tex]

ln( 1/2)  = t ln( [tex].5[/tex]  )

t = ln( .5)/ln( [tex].5[/tex]  )

t = 1

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