1) Bacteria at initial state=1000,8:00am
Bacteria at final state=100000
Tripled after 2.5hrs
The exponential form is;
100000=1000∗3(150t)
100=3(150t)
ln 100=150tln 3
150t=(ln 3ln 100)
t=(ln 3ln 100)∗150
t=628.77mins≈629mins
t=10hrs 29mins
Time =8.00 am+10hr 29 mins
=6.29pm
Population at 2.00pm
P=1000∗3(150t)
t=2.00pm -8.00am=6hrs=360mins
P=1000∗3(150360)
=41899.83
2)dtdN=kn
∫NdN=∫kdt
ln N=kt+C
Given for t=0, N=40million
⟹ln(40)=C
And for t=10, N=50million
ln(50)=k*10+ln(40)
k=101(ln 50−ln 40)=101ln (1.25)
Hence, ln (N)=101ln (1.25)t+ln (40)
For t=20
ln (N)=101ln (1.25)∗20+ln (40)
=ln (1.25)2+ln (40)=ln (40∗1.252)
N=40*1.252
=62.5million
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