SOLUTION: Hey, I was wondering you you solve radical equations such as this. 3 to the square root of 2x+3 = the square root of x-7 And also, what is a exponential decay?

Question 78884: Hey, I was wondering you you solve radical equations such as this.
3 to the square root of 2x+3 = the square root of x-7
And also, what is a exponential decay?
Answer by mathdoc314(58) (Show Source): You can put this solution on YOUR website!

I have never seen an equation like this solved. You could find some kind of numeric solver to find a numeric solution. I don't think you can do it with the kind of algebra most people know. Maybe Ramanujan would have been able to see it.
Exponential decay happens when something is disappearing at a rate that is proportional to the amount that is remaining. So as there is less and less of it, it disappears slower and slower. For example, if there is x amount of radioactive substance found in a material at the time it died, and the amount keeps decreasing by 0.003 per year (times the amount that there is), that is exponential decay. The equation looks like
x(t) = x(0) e^(-0.003 t)
where t is in years, and e^u is the exponential function, and e is the natural base for logarithms.

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