To answer this questions we must first find the constant k. If we find k then we can calculate our population for anytime.
I am going to assume that time t is measured in hours as the problem statement doesn't specify.
The population doubles every half hour, therefore:
p=5000 when t=0.5 hours
Plug these values in the equation to obtain:
5000=2500e^(0.5k)
Simplify...
2=e^(0.5k)
Square both sides
4=e^k
k=ln(4)
Now we have k so we can plug it in the original equation and obtain p for any time
p(t)=2500e^(ln(4)t), which simplifies to
p(t)=2500(4)^t
Now evaluate for t=100 minutes (1.67 hours) and t=4 hours
p(1.67)=2500(4)^1.67
p(1.67)=25315
p(4)=2500(4)^4
p(4)=640000
11/26/2013

Carlos T.