Applied Environmental Analysis Midterm 2

Why scaling variables is critical for PCA

Linear Function

y = mx + b

Exponential

𝑦 = 𝑦0 (1 + 𝑟)^t or 𝑦 = 𝑦0(𝑀)^{1+ t}

Slope Formula

Growth rate (r) formula

Multiplier (M) Formula

Power Function

𝑦 = 𝑘𝑥^c

Linear Difference Equation

𝑝(𝑛) = 𝑝(𝑛 − 1) − 20

Exponential difference equation

𝑝(𝑛) = 2𝑝(𝑛 − 1)

Linear solution equation:

𝑝(𝑛) = 150 + 20𝑛

Exponential solution equation:

𝑝(𝑛) = 150(0.927)ⁿ

Affine difference equation

𝑝(𝑛) = 1.018𝑝(𝑛 − 1) − 20

Affine Solution Equation

𝑝(𝑛) = 𝑎(0.75)ⁿ + 𝑏

Logistic Growth Function

(1 + r_max)p(n-1) - r_max / K * p(n-1)²

Harvest Model

Chaos Model

Systems model