some radioactive isotopes dacay at an exponential rate. this decay can be modeled through the function At = A0e^-rt, where At is the mass at any time t, A0 is the original amount, r is the decay rate constant, and the t is the time. in addition, each radioactive isotope has a half-life, which is the time it takes for an amount of the material to decrease by half. Using this equation, derive an equation that can be used to calculate the half-life of a certain material​