Question

A population of 40 deer are introduced into a wildlife sanctuary it is estimated that the sanctuary can sustain up to 500 dear absent constraints the population would grow 50% per year estimate the population after one year​

Answer 1

Answer:

There would be 60 deer after 1 year

Step-by-step explanation:

When a population is growing in a constrained environment with capacity K, and absent constraint grows exponentially with growth rate r, then the population behavior can be represents by the logistic growth model,

$P_n = P_{n-1}+ r(1-\frac{P_{n-1}}{K})P{n-1}$

Where,

$P_{n-1}$ = previous year population,

r = growth rate per year,

K = Capacity,

Here,

$P_0 = 40, r = 50\% = 0.50, K = 2000$

Thus, the population of deer after 1 year,

$P_1=40+0.50(1-\frac{40}{2000})40$

$=40+0.50(\frac{2000-40}{2000})40$

$=40+0.50(\frac{1960}{50})$

$=40+19.60$

$=59.6\approx 60$