SOLUTION: Why does the equation y=(0.5)^x not have an x- intercept, using algebra?

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Question 209800: Why does the equation y=(0.5)^x not have an x- intercept, using algebra?
Found 2 solutions by jsmallt9, vleith:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
X-intercepts are where a graph crosses the x-axis. The points on the x-axis have y-coordinates of zero. So the x-intercepts are the x-values that make the y-value zero.

In your equation, y+=+%280.5%29%5Ex, when will the y be zero? In other words, what is the solution to 0+=+%280.5%29%5Ex? Answer? Never! It is impossible for %280.5%29%5Ex to be zero (or negative for that matter). This is why there are no x-intercepts for the equation.

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
In order for a point to be an 'x-intercept', the y coordinate must be 0.
Let's substitute in y=0 and then attempt to solve for x
+y=%280.5%29%5Ex
Log%28y%29+=+x%2A+Log%280.5%29
Log%280%29+=+x%2ALog%280.5%29
The Log(0) is undefined, so y cannot be 0.
You can also try it another way
As x increases, the value of %280.5%29%5Ex approaches 0. However, 0 is the asymptote --> y never 'quite gets to 0, just really really close'