Answer:
Step-by-step explanation:
The population model describing the population of antelopes in the area is
Pn+1 = [1.75(Pn)^2/(Pn-1)] + 32 - Pn
where n represents the number of years.
In the first year, the number of antelopes is given as 89, to find the number of antelopes for the second year, it means we are looking for P(1+1) = P2. We will substitute 1 for n and 89 for Pn+1
It becomes
Pn+1 = [1.75(Pn)^2/(Pn-1)] + 32 - Pn
P2 = [1.75×89^2 / (89 - 1)] + (32 -89)
P2 = [13861.75 / 88] - 57
P2 = 101
To find P3, we will substitute 101 for Pn+1 and 2 for n. It becomes
P3 = [1.75×101^2 / (101 - 1)] + (32 -101)
P3 = [17851.75 / 100] - 69
P3 = 110
To find P4, we will substitute 110 for Pn+1 and 3 for n. It becomes
P4 = [1.75×110^2 / (110 - 1)] + (32 -110)
P4 = [21175 / 109] - 78
P4 = 116
To find P5, we will substitute 116 for Pn+1 and 4 for n. It becomes
P5 = [1.75×116^2 / (116 - 1)] + (32 -116)
P5 = [23548 / 115] - 84
P5 = 121
To find P6, we will substitute 121 for Pn+1 and 5 for n. It becomes
P6 = [1.75×121^2 / (121 - 1)] + (32 -121)
P6 = [25621.75 / 120] - 89
P6 = 125
To find P7, we will substitute 125 for Pn+1 and 6 for n. It becomes
P7 = [1.75×125^2 / (125 - 1)] + (32 -125)
P7 = [27343.75 / 124] - 93
P7 = 128
To find P8, we will substitute 128 for Pn+1 and 7 for n. It becomes
P8 = [1.75×128^2 / (128 - 1)] + (32 -128)
P8 = [28672 / 127] - 96
P8 = 130
To find P9, we will substitute 130 for Pn+1 and 7 for n. It becomes
P9 = [1.75×130^2 / (130 - 1)] + (32 -130)
P9 = [29575 / 129] - 98
P9 = 131
To find P10, we will substitute 131 for Pn+1 and 7 for n. It becomes
P10= [1.75×131^2 / (131 - 1)] + (32 -131)
P10= [30031.75 / 130] - 99
P10 = 132
The correct option is C
