Question

Community ecologists study the factors that determine the abundance of different species. The Abundance of three algae species (in mg/mL) is quantified in two different lakes before and after an unusually hot summer. The coordinates of these four samples inR3are (i) Lake A: (97,84,43)and (100,80,50) before and after summer, respectively, and (ii) Lake B: (23,59,22) and (20,63,15)before and after summer, respectively.(a) How does the magnitude of the change in algal community compare between the two lakes

Answer 1

Step-by-step explanation:

Given that:

The abundance of three algal species in Lake A is now represented by the vectors:

[97, 84, 43] and [100, 80, 50]

Now if we look at Lake A, the change occurring in the vector of algae species can be determined as:

a = [100 -97, 80 - 84. 50 - 43]

a = [3, -4, 7]

Thus, the magnitude of that change is:

`|a| = √((3)^2 +(-4)^2+(7)^2)`

`|a| = √(9+16+49)`

`|a| = √(74)`

`|a| =8.6 \ mg/mL`

The abundance of three algal species in Lake B is now represented by the vectors:

[25, 59, 22] and [20, 63, 15]

At Lake B, the change occurring in the vector of algae species can be determined as:

b = [20 -23, 63 - 59. 15 - 22]

b = [-3, -4, -7]

Thus, the magnitude of that change is:

`|b| = √((-3)^2 +(4)^2+(-7)^2)`

`|b| = √(9+16+49)`

`|b| = √(74)`

`|b| =8.6 \ mg/mL`

Hence, for both Lake A and B, the magnitude of change is the same.