Use a calculator to find an exponential curve f(x)=b*a^x that models the amount of iodine-131 remaining after x hours.
+33616 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-λ or a = e-ln(2)/τ (your choice!). Plug the numbers into a calculator to find the numerical value of a.
+33616 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-λ or a = e-ln(2)/τ (your choice!). Plug the numbers into a calculator to find the numerical value of a.
