Solve

Guides

0

Question

Open in App

Solution

Verified by Toppr

Then,

dNdt=kN where k is the proportionality constant.

dNN=kdt

∫NN0dNN=∫t0kdt

ln(NN0)=kt

N=N0ekt ...(i)

If N0=105 and t=2hours and

N=(1+10100)×105

=1.1×105

Hence

lnNN0=kt

ln(1.1×105105)=2k

ln(1.1)=2k

k=12ln(1.1)hours−1

=ln(√1.1)hours−1

Now

ln(NN0)=kt

N is now 2×105

Hence

NN0

=2×105105

=2

Thus

ln(NN0)=kt implies

ln2=ln√1.1t

ln2=ln(1.1)2t

2ln2=ln(1.1)t

t=ln4ln(1.1)

=14.54 hours

Was this answer helpful?

0