A certain isotope decays at a rate of 2%per 100 years. If t represent the time in years and y represent the amount of the isotope left then the equation for the situation is y=y0e^-0.0002t . In how many years will there be 86% of the isotope left? . Let x = initial amount then our formula is .86x = xe^(-0.0002t) . Notice, if we divide both sides by x, we eliminate our unknown: .86 = e^(-0.0002t) Solving for x, we take the ln of both sides: ln(.86) = -0.0002t ln(.86)/(-0.0002) = t 754.114 years = t
