A radioactive isotope R obeys the differential equation

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

\dfrac{dm}{dt}=k\,m

, where

m(t)

is the mass (in milligrams) remaining

t

days after an experiment begins. Laboratory records show that the sample had a mass of 200\,mg at

t=0

and 140\,mg exactly 5\,days later. (a) Determine the numerical value of the constant

k

and include appropriate units. (b) Using your value of

k

, calculate the number of days required for the sample to reach a mass of 50\,mg.