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# Match the parametric equations with the graphs (labeled I-VI). Give reasons for your choices.$x = \cos 8t$ , $y = \sin 8t$ , $z = e^{0.8t}$ , $t \ge 0$

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So for this problem 25 what we're being asked to do is to match Parametric equations with their appropriate graph. So the parametric equation we're given is that x of t equals co sign eight t and y of t equals sign 18. So essentially, what we have on our curves that lie on the cylinder of X squared post y squared equals one. Um, so basically what we have is a circle. However, we see that since Z equals E to the 0 80. Since this right here is exponential, it's going to increase exponentially. So what that means is, what we're going to have is almost like a spiral graph, whereas the X and Y is cause it to go in a circle. But the Z is actually going to cause it to move in the Z direction, since it's constantly increasing. So that is best represented by graph four. So graph four is going to be the best representation and the one that we can choose for these set this set of parametric equations

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