Exponential decay problem.

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).

[Dennis]

the constant is depending on the material, i don't think this task can be solved with the information provided.

[Torsten]

The amount left after 7 days in mg is

100*e^(k*7)

where the unit of k is in 1/day.

[Adnan Sardar]

Gallium-67, which has a half-life of 3.261 days.

[Jan]

@Adnan Sardar: This sounds like a homework question. So please show, what you have tried so far and ask a specific question. If somebody posts a solution, this thread can be considered as trial to cheat.

[Adnan Sardar]

syms k
k=solve(100==100*exp(k*0),k);
D7=100*exp(k*7)

[David Goodmanson]

Hi Adnan,

You are getting closer, you can do something similar but making use of the fact that the half life is 3.261 days.

[Adnan Sardar]

% 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]

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