Question

A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents the amount of the isotope left then the equation for the situation is

Answer 1

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

Answer 2

Answer:

y=y0e^-0.0002t

Step-by-step explanation: