Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 8% per day. A sample of this radioactive substance has an initial mass of 2.43 kg. Find the mass of the sample after three days. Round your answer to two decimal places.Note: This is a continuous exponential decay model.And though the decay rate parameter is 8% per day, the actual decay is not 8% each day.

Answer 1

Given:

Decay rate = 8% per day = 0.08

Initial mass = 2.43 kg

Let's find the mass of the sample after 3 days.

Apply the exponential decay formula:

`A=P_oe^(-rt)`

Where:

A is the final amount

Po is the initial amount = 2.43

r is the rate = 0.08

t is the time = 3 days.

Thus, we have:

`\begin{gathered} A=2.43e^(-0.08*3) \\ \\ A=2.43(0.78662) \\ \\ A=1.91 \end{gathered}`

Therefore, the mass of the sample after 3 days is 1.91 kg.

ANSWER:

1.91 kg