A certain radioactive isotope decays at a rate of 2% per 100 years. if t represents time in years and y represents the amount of
the isotope left then the equation for the situation is y=y0e-0.0002t . in how many years will there be 89% of the isotope left? round to the nearest year.
We rewrite the equation: y = y0 * e ^ (- 0.0002 * t) In this equation: I = represents the initial amount of the isotope We have then: 89% of the isotope left: 0.89 * y0 = y0 * e ^ (- 0.0002 * t) We clear the time: e ^ (- 0.0002 * t) = 0.89 Ln (e ^ (- 0.0002 * t)) = Ln (0.89) -0.0002 * t = Ln (0.89) t = Ln (0.89) / (- 0.0002) t = 582.6690813 round to the nearest year: t = 583 years Answer: There will be 89% of the isotope left in about: t = 583 years
