Answer:
1056
Explanation:
dP/dt = 0.0013P (1 − P/6200)
Euler's method states:
yₙ₊₁ = yₙ + Δt F(tₙ, yₙ)
Substituting:
P(t+1) = P(t) + (1) [0.0013 P(t) (1 − P(t)/6200)]
P(t+1) = P(t) + 0.0013 P(t) (1 − P(t)/6200)
We know that when t=0, P=1000.
P(1) = P(0) + 0.0013 P(0) (1 − P(0)/6200)
P(1) = 1000 + 0.0013 (1000) (1 − 1000/6200)
P(1) = 1001.1
Repeating the pattern, we get P(50) is:
P(50) = 1055.7
Rounded to the nearest whole number, P(50) = 1056.