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**+5 **

Iodine-131 decays according to the radioactive decay equation N/N_{0} = e^{-λx}, or N/N_{0} = e^{-ln(2)x/τ}, where N is amount, N_{0} 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/N_{0} by f(x), then b = 1 and a = e^{-λ} 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

#1**+5 **

Best Answer

Iodine-131 decays according to the radioactive decay equation N/N_{0} = e^{-λx}, or N/N_{0} = e^{-ln(2)x/τ}, where N is amount, N_{0} 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/N_{0} by f(x), then b = 1 and a = e^{-λ} 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