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3 years ago

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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.

1 answer:

olchik [2.2K]3 years ago

3 0

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

<u>Step-by-step explanation:</u>

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

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

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