Math Tutoring on Growth
In Math Tutoring, Recursive Relationships are excellent for describing simply and cleanly how a quantity is changing. However, they are not convenient for making predictions or solving problems that stretch far into the future. For that, a closed or Explicit Relationship is preferred.
If a quantity starts at size ‘P0’ and grows by ‘d’ every time period, then the quantity after ‘n’ time periods can be determined using either of these relations:
In this equation, ‘d’ represents the Common Difference - the amount that the population changes each time n increases by 1.
If a quantity starts at size ‘’ and grows by ‘’ (written as a decimal, r) every time period, then the quantity after ‘n’ time periods can be determined using either of these relations:
We call ‘r’ the Growth Rate. The term (1+r) is called the Growth Multiplier, or Common Ratio.
If a population is growing in a constrained environment with Carrying Capacity ‘K’, and absent constraint would grow exponentially with growth rate ‘r’, then the population behavior can be described by the Logistic Growth Model:
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1. What is Recursive and Explicit Relationship?
2. State Recursive and Explicit form of Linear & Exponential Growth?
3. Define Logistic Growth.
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