Exponential decay problem.

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Adnan Sardar
Adnan Sardar 2018-10-24
评论： David Goodmanson 2018-10-30
Radioactive decay is modeled with the exponential function f(t)=f(0)e^(kt), where t is time, f(0) is the amount of material at t=0, f(t) is the amount of material at time t, k is a constant. If 100 mg are present at t=0, determine the amount that is left after 7 days. Material is Gallium-67, which has a half-life of 3.261 days. Write a script file for the problem. The program should first determine the constant k, then calculate f(7).
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Adnan Sardar
Adnan Sardar 2018-10-30
% k = constant
% D7 = amount of Gallium-67 left after 7-days (grams)
format compact
syms k
k=solve(50==100*exp(k*3.261),k);
D7=round(double(100*exp(k*7)),1)
David Goodmanson
David Goodmanson 2018-10-30
For sure. I would round D7 to two decimal places giving you four significant figures, since the half life that was provided has four sig figs. Lots of people are using symbolic calculation now but in this case taking the log of both sides gives
1/2 = exp(k*t_half)
log(1/2) = k*t_half
k = log(1/2)/t_half

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