Question

(TIMED HELP) The population model describing the population of antelope in an area is:

Answer 1

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