Question

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For a certain radioactive element the growth rate is -0.377 when t is measured in days. If the inital amount is 500 grams how much would there be in 2.4 days?

Answer 1

In this case, the decay rate is -0.377 and the initial amount is 500 grams.

Therefore, there would be approximately 373.95 grams of the radioactive element remaining after 2.4 days.

Step-by-step explanation:

To find the amount of a radioactive element after a certain time, we can use the formula:

amount remaining = (amount initial) × e^(-λt)

Where:

• amount remaining is the final amount of the radioactive element
• amount initial is the initial amount of the radioactive element
• λ is the decay rate constant
• t is the time in days
• e is the base of natural logarithms, approximately 2.71828

In this case, the decay rate is -0.377 and the initial amount is 500 grams. To find the amount after 2.4 days:

1. Convert the decay rate to its positive value: 0.377
2. Plug in the values into the formula: amount remaining = 500 * e^(-0.377 * 2.4)
3. Calculate the value : amount remaining ≈ 373.95 grams

Therefore, there would be approximately 373.95 grams of the radioactive element remaining after 2.4 days.