Find the General Solution of the Difference Equation $\mathrm { y } _ { \mathrm { k } } = \mathrm { k } ^ { 2 }$

question 7

Multiple Choice

Find the general solution of the difference equation.
-Given that the signal $\mathrm { y } _ { \mathrm { k } } = \mathrm { k } ^ { 2 }$ is a solution of the given difference equation, find a description of all solutions of the equation. $\mathrm { y } \mathrm { k } + 2 + 6 \mathrm { y } \mathrm { k } + 1 - 7 \mathrm { yk } = 16 \mathrm { k } + 10$ for all $\mathrm { k }$

• A) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( - 7 ) ^ { \mathrm { k } }\)
• B) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } ( - 1 ) ^ { \mathrm { k } } + \mathrm { c } _ { 2 } ( 7 ) ^ { \mathrm { k } }\)
• C) \(\mathrm { k } ^ { 2 } + \mathrm { c } _ { 1 } + \mathrm { c } _ { 2 } ( - 6 ) ^ { \mathrm { k } }\)
• D) \(c _ { 1 } + c _ { 2 } ( - 7 ) ^ { k }\)

Identify how adaptations that were once advantageous can become maladaptive in a changed environment.

Describe the essentials of evolutionary change according to Darwin.

Understand the role and study of epigenetics in behavior.

Compare and contrast adaptations, genetic mutations, and other key evolutionary concepts.

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