Beginner4 equations~6 hours

Biology and Life Systems

Growth, genetics, ecology, and evolution.

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1
Hardy-Weinberg Equation
Intermediate
$p^2 + 2pq + q^2 = 1$
Allele frequencies remain constant across generations under ideal conditions.
Biological Sciences
Genetics
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2
Logistic Growth Equation
Intermediate
$\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$
Population grows exponentially at first, then slows as it approaches carrying capacity K.
Biological Sciences
Ecology
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3
Lotka-Volterra Equations
Advanced
$\frac{dx}{dt} = \alpha x - \beta xy, \quad \frac{dy}{dt} = \delta xy - \gamma y$
Predator-prey populations oscillate—prey growth minus predation, predators grow from eating prey.
Biological Sciences
Ecology
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4
Exponential Growth
Beginner
$N(t) = N_0 e^{rt}$
Population doubles repeatedly at a constant proportional rate.
Biological Sciences
Ecology
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