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,
[tex]P_n = P_{n-1}+ r(1-\frac{P_{n-1}}{K})P{n-1}[/tex]
Where,
[tex]P_{n-1}[/tex] = previous year population,
r = growth rate per year,
K = Capacity,
Here,
[tex]P_0 = 40, r = 50\% = 0.50, K = 2000[/tex]
Thus, the population of deer after 1 year,
[tex]P_1=40+0.50(1-\frac{40}{2000})40[/tex]
[tex]=40+0.50(\frac{2000-40}{2000})40[/tex]
[tex]=40+0.50(\frac{1960}{50})[/tex]
[tex]=40+19.60[/tex]
[tex]=59.6\approx 60[/tex]
The population after one year is 60 deer
Using this formula
A = P(1+r)^t
Where:
A=Amount
P=Initial value
R =Rate
T=Time
Let plug in the formula
A = 40(1+0.50)^1
A=40(1.50)^1
A=40(1.50)
A= 60 deer
The population after one year is 60 deer.
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