Question

If I could please have some guidlines on how to do this, I would greatly appreciate it! I'm totally lost!

1. Calculate the population size (N) at the given time (t) with either r or R below: Calculate r or R from the given R or r as well. 50 0.15 d) Generation Time Starting (t = 0) (year) (t) No a) 1000 b) 100 50 100 1000 100 100 100 100 0.25 ||| lalala 0.35 -0.15 0.45 0.35

Answer 1

Answer is provided below:

No = Initial population size t = time (generation) Nt = Population after generation t R = Net reproductive rate. r = Per capita growth rate In Exponential growth, Ne = Nox Rt If we consider percapita growth rate, er Then dN = RN dN = rat en N = rette e enn - erette N = ert, e we when it =0 N = No. rxo. - exec -ee . Nor et rt Nt - Noé N t=3, No - 1000, R = 0.4 (6) ..No = No X REN 1000 x(0.4)3 = 164 += 25, No = 50 R = 2.5 I NE = 50 x(2.5,25 = 14.44X10"] (c) 0.15825 3.75 oxe t = 25. No = 100, r=0.15 x 0.15x25 . Nt = Noxeret 100xe 3.75 = 1ooxe = 100 x 42.52 -- 42527

N = Nox Ry 4252 = 100 x R25 R 25 - 42-52 R = 252 42.52 = 11.162] 25 ® t=3, No = 1000, Nt - 64 64 = 1000 x ert rx3 64 - = 0.064 looo - 3r = en(0.064) = -2.75 r= -2.75 - 1-0.918] Se zx3 e 50 50 4.44 x 10 = 50 xerx25 → 2252 4.44 xID" > 2592 - en ( 4.44X10") - 22.971 > or = 220981 -0.92] (d) 2 - t=25, No=t00 50 R=6 Nt = 50x625 1.42 X1020 ert- en (N) = ln (142x10-1) = 44.8 → 25% = 44.8 >> = 423 8 -10792] t=10, No = 100 , r=0.25 Nt = 100 x eº-25X10 = 100 xe2.5 =112181 Rt = 1218 = 1812-18 RO = 12.18 > R= 10/12.18 = [1.284] 25

- 125 O.U 5 t=3, No = 1000 , R =0.5 Nt = 1000x (0.5) - 125 ert = 125 = 0.125 2x3 = en (0.125) = -2.08 ra - 2.08 -0.693 ) .03 r = & t= 10 No=100, r = 0.35 Nt = 100x 2035x10 - 100x23.5 - 3312] RlO 3312-337 33-12 R=10833.12 = 11:42] 100 th) t=2 , No=100 , or = – 0.15 N = 100 x eo.5*2 = 100 x0.741 - 24 R² = 72 = 0.74 R = √0.74 - 10.86 . 4 (00 (i) t=20, No -100 , r = 0.45 NA - 100x eº-45 * 20 . 100 X 8103.1 - [810310 220810310 78103.1 R = 2958103.1 = 1.568] 100 t = 20, No 1oo , r = 0.35 NA - 100 x 0.35*20 - 100X1096.63 -109663 R20 109663 =1096-63 191096-63 - 1.419| too - 1096-63