Explanation Given information: Ricker difference function with harvest included x t + 1 = c x t e − x t − h x t → is the population size at time t c → per capita reproductive output As t → ∞ the population size approaches to x The number of individuals are harvested in each time step is represented by h Formula used: Taylor’s series expansion: f ( x ) = f ( a ) + f ' ( a ) ( x − h ) + , , , , , , , , , , , Calculation: Consider the Ricker difference function x t + 1 = c x t e − x t From previous problem we have, The x in terms of the growth factor c is x = ln c x ( 0 ) = ln c The derivative of x with respect to h is x ' ( h ) = d x d h = 1 c ( 1 − x ) e − x

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Chapter 3.8, Problem 4P

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To find: the linearization of x(h) at h=0.

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Chapter 3.8, Problem 3P

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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the linearization of x ( h ) at h = 0.

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Chapter 3 Solutions