Graphing with Mathematica and Parameters

Automaton2000
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Homework Statement



Problem.jpg


Second part of Part C is: Use mathematica to draw graphs for a few values of the parameters. [ Consider the cases b > 0 and b< 0]

Homework Equations


I think you use the answer to Part A
PartA.jpg




The Attempt at a Solution


Not sure how to graph with mathematica with parameters
 
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You don't, that's why it says "for a few values of the parameters."

So you can use your favorite method to assign the parameters,
varying from the ugly
Code:
a = 1;
b = -1;
A = 6;
Plot[P[t], {t, .., ...}]
or the better
Code:
Block[
 {a = 1, b = -1, A = 6},
 Plot[P[t], {t, .., ...}]
]
to my preferred
Code:
Plot[P[t] /. {a -> 1, b -> -1, A -> 6}, {t, .., ...}]

Using something like
Code:
Plot[P[t] /. {a -> {1, 2, 3, 4}, b -> 1, A -> -2} // Evaluate, {t, 1, 
  6}]
you can even plot multiple ones in the same plot.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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