Suppose 600g of a radioactive substance are present initially and 3 years later only 300g
remains.
If the equation modelling the change in mass of the radioactive substance is y = y0*e^(kt)
a. What does y0 represent, and what is its value, based on the problem’s statement (above)?
b. Is this problem about exponential growth or exponential decay? Explain.
c. What does k represent and what is going to be its sign (positive or negative)? Explain.
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a. y0 represents the initial amount of the radioactive substance, which in this case is 600g.
b. This problem is about exponential decay because the amount of the substance is decreasing over time.
c. k represents the rate of decay of the radioactive substance. Since the substance is decaying, k will be negative. The negative sign indicates that the substance is decreasing in mass over time.
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