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Insecticide resistance If the frequency of a gene for insecticide resistance is $p($ a constant), then its frequency in the next generation is given by the expression$$f=\frac{p(1+s)}{1+s p}$$where $s$ is the reproductive advantage this gene has over the wild type in the presence of the insecticide. Often the selective advantage $s$ is very small. Approximate the frequency in the next generation with a linear approximation, given that $s$ is small.
$L(x)=p+p(p-1)(x-a)=p+p(p-1) s$
Calculus 1 / AB
Chapter 3
Derivatives
Section 8
Linear Approximations and Taylor Polynomials
Oregon State University
Harvey Mudd College
University of Nottingham
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this question asks us to approximate the frequency in the next generation using weatherization. What? We know that the first step is let's plug in half of a given the fact that a zero we end up with simply p because this is just Pete times one. And this is just divide by one because this is zero on the stair. Now take the derivative of prime of X and we get P times one plus SP minus P squared times one plus s prime. Remember, prime means the derivative and then plug in F prime A. So everywhere where you have axe plug in zero toe all these places and we now have he minus p squared. So our l of axe is gonna be he plus p times p minus one s. So this Alumax equation would be our model for the frequency of this or problem
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