Worksheet 2-4

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School

Arizona State University *

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Course

5A

Subject

Mathematics

Date

Jun 5, 2024

Type

pdf

Pages

6

Uploaded by BarristerWorldYak40

Names and ID Numbers Math 5A Unit 2 - Worksheet 4 1. (a) Go to this Desmos link. Use the sliders for a , h , and k to change the values of α , β , and γ (displayed below the sliders) until you get a nonlinear selection function you like. Note that γ (gamma) is written as ’g’ in Desmos. Write down your function below in the form w ( z ) = α + βz + 1 2 ( γ ) z 2 (b) What type of animal’s relative fitness could be described by your nonlinear selection function? Why? (c) Based on your function, if an animal has a weight of 14 kg, would losing weight or gaining weight be beneficial to its survival? Why? 1
(d) Using your function, find the average rate of change in the relative fitness when an animal’s weight increases from 15 to 17 kg. Write a sentence interpreting the result. (e) Using your graph in Desmos, determine the weight that maximises the animal’s relative fitness, and the maximum relative fitness. How do you think you can prove this using your equation alone and not the graph in Desmos? 2
(f) Find the instantaneous rate of change in relative fitness of an animal weighing 10.5 kg. Write a sentence to interpret what this means in the context of this problem. (g) Find the vertex of your function from Exercise 1, which will have the form ( z, w ( z ) = ( weight , relative fitness ), and then find the instantaneous rate of change in relative fitness of an animal that weighs as much as the z -coordinate of the vertex. (h) What do you notice about the result in part (g)? Why do you think this is the case? 3
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