After half hour=30 min you have 2×2500=5000 bacteria so you can use this into your equation to write:
\(5000=2500 e^{30k}\)
and:
\(e^{30t}= \frac{5000}{2500}=2\)
Apply the natural logarithm ln to both sides and get:
\(30t=ln(2)\)
so \(k=0.0231\) in units of \(\frac{1}{min}\)
so your equation is now:
\(p(t)=2500 e^{0.0231t}\)
1] it t= 50 min substituting you get:
\(p(50)=2500 e^{0.0231*50}=7935\) bacteria
2] if t= 8 h = 480 min you get:
\(p(480)=2500 e^{0.0231*480}=1.6* 10^{8}\) bacteria
