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# Use a calculator to find an exponential curve f(x)=b*a^x that models the amount of iodine-131 remaining after x hours.

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Use a calculator to find an exponential curve f(x)=b*a^x that models the amount of iodine-131 remaining after x hours.

Guest Sep 27, 2014

#1
+26625
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Iodine-131 decays according to the radioactive decay equation N/N0 = e-λx, or N/N0 = e-ln(2)x/τ, where N is amount, N0 is initial amount, x is time, λ is the decay constant and τ is its half-life  (λ = ln(2)/τ).  For Iodine-131 the half-life is approximately 192.5 hours.

So, if we replace N/N0 by f(x), then b = 1 and a = e or a = e-ln(2)/τ  (your choice!).  Plug the numbers into a calculator to find the numerical value of a.

Alan  Sep 27, 2014
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#1
+26625
+5

Iodine-131 decays according to the radioactive decay equation N/N0 = e-λx, or N/N0 = e-ln(2)x/τ, where N is amount, N0 is initial amount, x is time, λ is the decay constant and τ is its half-life  (λ = ln(2)/τ).  For Iodine-131 the half-life is approximately 192.5 hours.

So, if we replace N/N0 by f(x), then b = 1 and a = e or a = e-ln(2)/τ  (your choice!).  Plug the numbers into a calculator to find the numerical value of a.

Alan  Sep 27, 2014
#2
+85614
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Very nice, Alan !!!!!

CPhill  Sep 27, 2014

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