Yuri O. answered • 02/12/21

16 years online, 464 former SAT problems drilled down

We will use the equation for the decay of radioactive materials:

N = N_{o} e^{-λt}

N - the amount of radioactive material left

N_{o} - the initial amount of radioactive material at time zero

λ - decay coefficient

t - time

λ = 0.693/T_{1/2}

T_{1/2 }- half time of radioactive material

Calculating λ:

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)