Exponential Decay: Calculating Radioactive Compound Decay

How can we determine the amount of a radioactive compound that remains after a certain period of time?

Given data: A radioactive compound with mass 430 grams decays at a rate of 28% per hour. Which equation represents how many grams of the compound will remain after 5 hours? Options: A.c = 430(1 + 0.28)^5 B.c = 430(1 - 0.28)^5 C.c = 430(0.72)^5 D.c = 430(1.28)^5

Answer:

The correct equation representing the decay of radioactive compound over 5 hours is: c = 430(1 - 0.28)^5

This question pertains to radioactive decay processes and it can be solved using the concept of exponential decay in mathematics. The general equation for radioactive decay is c= P(1-r)^t, where 'c' is the remaining amount of substance, 'P' is the initial amount of substance, 'r' is the rate of decay, and 't' is time. In the provided scenario, the initial mass 'P' is 430 grams, the rate 'r' of decay is 28% (or 0.28 when expressed as a decimal), and the time 't' is 5 hours.

Substituting these values in the equation, the correct equation is: c = 430(1 - 0.28)^5. Thus, the correct option from the given alternatives is Option B: c = 430(1 - 0.28)^5. This equation shows how much of the radioactive compound will remain after 5 hours.

Understanding exponential decay is crucial in various fields such as physics, chemistry, and biology. It helps us predict the decay process of radioactive substances and other natural phenomena over time. By utilizing the formula and concepts of exponential decay, we can make accurate calculations and predictions regarding the decay rate of substances.

For further clarification and examples on exponential decay, you can explore resources like textbooks, online tutorials, and educational platforms. Enhancing your understanding of exponential decay will enable you to tackle more complex problems and applications in different scientific disciplines.