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Type: Multiple-Choice
Category: Algebraic Expressions
Level: Grade 10
Standards: HSA-SSE.A.1, HSA-SSE.A.1b
Author: nsharp1
Created: 5 years ago

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Algebraic Expressions Question

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Grade 10 Algebraic Expressions CCSS: HSA-SSE.A.1, HSA-SSE.A.1b

One way the rate of population growth (how fast or slowly a population is growing) can be modeled is by the expression

$r N ((K-N)/K)$ , where

$N$ is the size of the population,

$K$ is a constant which describes the maximum population that a certain geographic region can support, and

$r$ is a positive constant that relates to the maximum growth rate. If the population of a certain species is growing and becomes very close to the carrying capacity, what will happen to the rate of growth and why?

The growth rate of the population will diminish, because $N~~K$ , and so $(K-N)/K$ will approach zero.
The population will grow more rapidly, since both $N$ and $K$ become large.
The population growth rate will remain the same, since the parameter $K$ is found in both the numerator and denominator, and thus any increase or decrease in its value will cancel out.
This cannot be determined without knowing specific numerical values for $r, K,$ and $N$ .