Question

Suppose the population of a colony of ants grows at the rate:
P’(x) = 1 + 5/sqroot(t+1)

If there are 250 ants after 120 hours, what was the population at t=0?

Answer 1

dP/dt = 1+5/√(t+1)
dP = (1 + 5/√(t+1)) dt
P = t + 10√(t+1) + c
now plug in (120,250) to find c and then plug in t=0