The "Verhulst Model" for Population Growth Specifies the Reproductive Rate $R ( p ) = \frac { r } { 1 + k p }$

question 38

Multiple Choice

The "Verhulst model" for population growth specifies the reproductive rate of an organism as a function of the total population according to the following formula: ? $R ( p ) = \frac { r } { 1 + k p }$
Where p is the total population in thousands of organisms, r and k are constants that depend on the particular circumstances and organism being studied, and R(p) is the reproduction rate in thousands of organisms per hour. If $k = 0.075$ and $r = 35$ , find $R ^ { \prime } ( p )$ .

• A) \(\frac { 2.625 } { 1 + 0.075 p ^ { 2 } }\)
• B) \(\frac { 35 } { 1 + 0.075 p ^ { 2 } }\)
• C) \(\frac { 2.625 } { ( 1 + 0.075 p ) ^ { 2 } }\)
• D) \(\frac { 2.625 } { 1 + 0.075 p }\)
• E) \(- \frac { 2.625 } { ( 1 + 0.075 p ) ^ { 2 } }\)

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