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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.

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Answer:  [tex]\bold{G(t)=356e^{-0.59413t}}[/tex]

Step-by-step explanation:

Use the decay formula: [tex]P=P_oe^{kt}[/tex]   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)

[tex]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[/tex]

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

              [tex]\large\boxed{P=356e^{-0.59413t}}[/tex]

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