Answer:
121
Step-by-step explanation:
dP/dt is propotional to P^½
dP/dt = k(P^½)
When P=100, dP/dt=+20
20 = k(100^½)
20 = 10k
k = 2
dP/dt = 2(P^½)
Reciprocate both sides:
dt/dP = 1/[2(P^½)]
dt/dP = ½[P^(-½)]
Integrate wrt P.
t = ½ [(P^½) ÷ ½] + c
t = P^½ + c
Using t = 0, P =100.. find c
0 = 100^½ + c
0 = 10 + c
c = -10
t = P^½ - 10
Find P when t=1
1 = P^½ - 10
P^½ = 11
P = 121
