(1 point) The time rate of change of a rabbit population P is proportional to the square root of P. At time t=0 (months) the population numbers 100 rabbits and is increasing at the rate of 10 rabbits per month. Let P′=kP12 describe the growth of the rabbit population, where k is a positive constant to be found. Find the formulas for k and for the rabbit population P(t) after t months.

2√P = t + 20

Step-by-step explanation:

Rate of change of a rabbit population ∝ √P

-----(1)

At time 't' = 0 the population of the rabbits (P) = 100 and rabbits per month.

We plug in the values in the equation (1),

k = 1

Equation (1) becomes,

By the integration of this equation,

Again for t = 0 and P = 100,

C = 20

Now the integrated equation will be,

Therefore, formula representing population P after time t is,

2√P = t + 20