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C175 - Data Management Foundations


Last updated: May 4th, 2023

Input and Output

Function Types

Function Type Example Function Input (Substitute) Output (Solution) Keywords
Linear 𝐿(𝑥) = 3𝑥 - 5 𝐿(5) 10 Constant Rate
Polynomial 𝑃(𝑥) = -2𝑥2 + 3𝑥 + 5 𝑃(5) -30 Constant Acceleration
Exponential 𝐸(𝑥) = 2𝑒-0.5𝑥 𝐸(5) 0.16 Constant Ratio
Logistic 𝐿(𝑥) = 10000/(1 + 5𝑒-0.2𝑥) 𝐿(5) 3521.87 Stabilize/limit
  • The cause is the input and the effect is the output
    • Effect(Cause)
  • References to time will need to be converted to a 24 hour clock.

Rate of Change

  • Instantaneous Rate of Change
    • The change at a specific time
  • Average Rate of Change
    • 𝑦2 − 𝑦1 / 𝑥2 − 𝑥1

Concavity

  • Concave Up is a u
  • Concave Down is an n

Modelling

  • Strong
    1. Find the furthest left 𝑥-value and the furthest right 𝑥-value
    2. Right 𝑥-value minus left 𝑥-value
    3. Extend the range of the data from 50% on the left and right.
      Note: If you go beyond the range, a prediction can't be made.
    4. Left 𝑥-value: 20
      Right 𝑥-value: 40
    5. 40 − 20 = 20
    6. (20)(0.50) = 10
    7. Range for extrapolation is from 10-50
  • Moderate
    1. Find the furthest left 𝑥-value and the furthest right 𝑥-value
    2. Right 𝑥-value minus left 𝑥-value
    3. Extend the range of the data from 25% on the left and right.
      Note: If you go beyond the range, a prediction can't be made.
    4. Left 𝑥-value: 20
      Right 𝑥-value: 40
    5. 40 − 20 = 20
    6. (20)(0.25) = 5
    7. Range for extrapolation is from 15-45
  • Weak
    1. Do not make prediction

Interpolation: Interpolation allows one to make a prediction for a situation or time within the given points in a data set.

Extrapolation: Extrapolation allows one to make a prediction for a situation or time that extends beyond the given points in a data set.

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