Let p denote the number of paramecia in a nutrient solutiont days after the start of an
Chapter 3, Problem 57(choose chapter or problem)
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
\(0=\ln p+0.83-\ln (2.3-0.0046 p)-2.3 t\)
Use implicit differentiation to show that the rate of change of \(p\) with respect to \(t\) satisfies the equation.
\(\frac{d p}{d t}=0.0046 p(500-p)\)
Equation Transcription:
Text Transcription:
P
T
P
T
0=lnp+0.83 -ln(2.3-0.0046p)-2.3t
dpdt=0.0046p(500-p)
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