Suppose initial mass of Radioactive substance is m0.
Rate of decay of radioactive substance at time t is
dmdt∝m
∴dmdt=−k(m)
(Here k is constant of variance and substance looses it mass hence sign is negative)
∴dmm=−k dt
∴∫1mdm=−k∫1dt
∴logm=−kt+logc
∴logm−logc=−kt
∴log(mc)=−kt
∴mx=e−kt
∴m=c⋅ekt
Now at t=0(at the initial time) mass m=m0
∴m0=ce−k(0)
∴x=m0
∴m=m0e−kt .(1)
Now at t=1 hour mass m=90 gram
∴90=m0e−k(0) ..(2)
Now at t=2 hours mass m=60 gram
∴60=m0e−2k .(3)
Taking result (2) ÷ result (3)
∴9060=m0e−km0e−2k
∴32=ek
We find initial mass m0 from equation (2)
90=m0(32)−1
∴90=m0(23)
2702=m0
∴135=m0
∴ Initial mass of the radioactive substance is 135 gram.