An initial amount of radioactive substance y0 is given, along with information about the remaining after a given time t in appropriate units. For an equation of the form y = y0ekt that models the situation, give the exact value of k in terms of natural logarithms: y0 = 8.1 kg; after 4 yrs, 0.9 kg remain. A common use of exponential functions is to model radioactive decay. If we know the half-life of a substance, we know how long it takes for a substance to reach half of its initial amount. It will continue to halve repeatedly, something that is best modeled using an exponential function: y=y0e^(kt)
Note that the value of k must be negative. If it were positive, this would be modeling growth instead of decay.