Chapter 3.2, Problem 57ES

Let $p$ denote the number of paramecia in a nutrient solution $t$ days after the start of an experiment, and assume that $p$ is defined implicitly as a function of $t$ by the equation

$0=\ln p+0.83-\ln \left(2.3-0.0046p\right)-2.3t$

Use implicit differentiation to show that the rate of change of $p$ with respect to $t$ satisfies the equation

$\frac{dp}{dt}=0.0046p\left(500-p\right)$