 ## Tutoring on Growth

Learning Objectives:

#### Understand application of Linear, Exponential and Logistic Growth.

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.

Linear Growth:

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:

Recursive Form:  Explicit Form: In this equation, d represents the Common Difference - the amount that the population changes each time n increases by 1.

Exponential Growth:

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:

Recursive Form: Explicit Form: We call r the Growth Rate. The term (1+r) is called the Growth Multiplier, or Common Ratio. Logistic Growth:

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: Learn ‘Growth’ with AffordEdu.

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Hook questions:

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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