Modeling with first order linear differential equations

DODGEVIPER13
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Homework Statement


uploaded file (Problem 5)

Homework Equations


uploaded file

The Attempt at a Solution


Ok so I think I have the correct answer but the problem is I don't know how to solve for the actual answer with 2 equations which one do I plug into? Sorry for all the erasing!
 

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Oh an the 1400000 is suppose to be there sorry it is so light and I solved the t = 71.7994 using wolfram.
 
Uggg no replies, I guess my problem was too long or something?
 
Can someone please help me out I don't think it is too outrageous I have already done the work it is quite literally just plugging and playing from here my question simply is first did I get the set up right and if I did then what do I plug in at the end?
 

Thread 'Finding the nth roots of a complex number'

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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