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)}`

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))\\\\\\(44.5)/(356)=e^(3.5k)\\\\\\0.125=e^(3.5k)\\\\\\ln(0.125)=3.5k\\\\\\(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)}`