Question

current objective
calculate continuous growth and decay
question
a radioactive substance has a continuous decay rate of 0.056 per minute. how many grams of
a 120 gram sample will remain radioactive after 40 minutes? round the answer to the nearest
tenth of a gram, and do not include the unit in your answer.
provide your answer below:
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Explanation:

Step1: Identify the formula

The formula for continuous decay is \( A = A_0e^{-rt} \), where \( A_0 \) is the initial amount, \( r \) is the decay rate, and \( t \) is the time.

Step2: Substitute the values

Given \( A_0=120\), \( r = 0.056\), and \( t = 40\). Substitute into the formula: \( A=120e^{-(0.056\times40)} \).
First calculate \( 0.056\times40 = 2.24\). So \( A = 120e^{- 2.24}\).

Step3: Calculate \( e^{-2.24}\)

Using a calculator, \( e^{-2.24}\approx0.1065\).

Step4: Calculate \( A\)

\( A=120\times0.1065 = 12.78\approx12.8\)

Answer:

\(12.8\)