## Precalculus: Mathematics for Calculus, 7th Edition

$R = k \cdot \dfrac{P^2t^2}{b^3}$ where k = constant of proportionality
RECALL: (i) If the quantities (or variables) $x$ and $y$ are related by the equation $y=kx$, then $y$ is directly proportional to $x$, where $k$ is the constant of proportionality. (ii) If the quantities (or variables) $x$ and $y$ are related by the equation $y=\dfrac{k}{x}$, then $y$ is inversely proportional to $x$, where $k$ is the constant of proportionality. $R$ is given to be directly proportional to the product of $P^2$ and $t^2$ and inversely proportional to $b^3$ therefore the equation that expresses the given statement is: $R = k \cdot \dfrac{P^2t^2}{b^3}$ where k = constant of proportionality