Question

At the beginning of an experiment, a scientist has 356 grams of radioactive goo. After 210 minutes, her sample has decayed to 44.5 grams. Find a formula for G ( t ) , the amount of goo remaining at time t . Keep at least 5 decimal places.

Answer 1

Answer:  $\bold{G(t)=356e^{-0.59413t}}$

Step-by-step explanation:

Use the decay formula: $P=P_oe^{kt}$   where

• P is the remaining amount of the sample
• P₀ is the original amount of the sample
• k is the decay rate
• t is the time (in hours)

Given: P = 44.5, P₀ = 356, k = unknown, t = 210 minutes (3.5 hours)

$44.5=356e^{k(3.5)}\\\\\\\dfrac{44.5}{356}=e^{3.5k}\\\\\\0.125=e^{3.5k}\\\\\\ln(0.125)=3.5k\\\\\\\dfrac{ln(0.125)}{3.5}=k\\\\\\-0.59413=k$

Input P₀ = 356 and k = -0.59413 into the decay formula

              $\large\boxed{P=356e^{-0.59413t}}$