We will use the equation for the decay of radioactive materials:
N = No e-λt
N - the amount of radioactive material left
No - the initial amount of radioactive material at time zero
λ - decay coefficient
t - time
λ = 0.693/T1/2
T1/2 - half time of radioactive material
There will be 35 days in 5 weeks.
λ = 0.693/35 = 0.0198
Writing the equation:
30 = 175 • e-0.0198t → divide by "175"
(30/175) = e-0.0198t → take ln
ln(30/175) = ln(e-0.0198t)
-1.76358859 = -0.0198t
t = 89.07 (days) or approximately 12.72 (weeks)