Math  /  Calculus

QuestionGiven the Beverton-Holt model R(Nt)=R01+aNtR(N_t)=\frac{R_0}{1+a N_t} with a=0.05a=0.05, R0=5R_0=5, find NtN_t for t=1,2,,5t=1,2,\ldots,5 and limtNt\lim_{t \to \infty} N_t for N0=2N_0=2.

Studdy Solution
Calculate the value of $$.
=±+0.=±20. = \frac{- \pm \sqrt{ +}}{0.} = \frac{- \pm \sqrt{2}}{0.}Since $$ must be positive, we take the positive root.
=+20.=101025.86 = \frac{- + \sqrt{2}}{0.} =10 -10\sqrt{2} \approx5.86So, the population for t=,2,3,,5t=,2,3,,5 is 9.09,6.88,5.32,5.59,5.719.09,6.88,5.32,5.59,5.71 respectively, and limtNt5.86\lim{t \rightarrow \infty} N_{t} \approx5.86.

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