Question

Logistic Growth While population growth is often modeled by exponential functions, Pierre Verhulst proposed the logistic model in 1836 to account for the limit of growth in a biological system, due to limited resources. The logistic model is based on the equation $frac{dP}{dt} = rP(1 - frac{P}{k})$ where $P$ is population at time $t$, and $r$ and $k$ are constants related to the particular biological system. 6. Looking at the differential equation; what happens to the growth rate $frac{dP}{dt}$ as P approaches k?

          Logistic Growth
While population growth is often modeled by exponential functions, Pierre Verhulst
proposed the logistic model in 1836 to account for the limit of growth in a biological
system, due to limited resources. The logistic model is based on the equation
$frac{dP}{dt} = rP(1 - frac{P}{k})$ where $P$ is population at time $t$, and $r$ and $k$ are constants related to
the particular biological system.
6. Looking at the differential equation; what happens to the growth rate $frac{dP}{dt}$ as
P approaches k?

$Logistic Growth While population growth is often modeled by exponential functions, Pierre Verhulst proposed the logistic model in 1836 to account for the limit of growth in a biological system, due to limited resources. The logistic model is based on the equation fracdPdt = rP(1 - fracPk) where P is population at time t, and r and k are constants related to the particular biological system. 6. Looking at the differential equation; what happens to the growth rate fracdPdt as P approaches k?$

Added by Vernon R.

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