Answer:
k = 1
P(t) = (t + 20)²
Step-by-step explanation:
P' = k√P = k P⁰•⁵
To solve for k,
P' = 10 rabbits/month
P = 100 rabbits
10 = k √100
10 = 10k
k = 1
To solve for P(t)
P' = dP/dt
(dP/dt) = kP⁰•⁵
dP/P⁰•⁵ = k dt
P⁻⁰•⁵ dP = k dt
∫ P⁻⁰•⁵ dP = ∫ k dt
2P⁰•⁵ = kt + c
At t = 0, P = 100
2(100)⁰•⁵ = 0 + c
2 × 10 = c
c = 20
2P⁰•⁵ = kt + c
2P⁰•⁵ = kt + 20
Recall, k = 1
2P⁰•⁵ = t + 20
P⁰•⁵ = (t + 20)
P(t) = (t + 20)²
