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

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) $- \frac { 2.625 } { ( 1 + 0.075 p ) ^ { 2 } }$