Expert: Sherry Wallin - 12/24/2010

Question
Hello Ms.Sherry,
      How are you? Good!? I am unable to understand one question from my textbook! It says:- Use the graph of y = 3^x to find the approximate value of each power!
    1) 3^(1.5)
    2) 3^(0.5)
    3) 3^(-0.25)
I can not understand how the graph can be used to determine the approximate values of each power!Can you please explain me?
                         ThankU SO Much!!!!!

Answer
Xiang~

Do you know what y=3^x looks like? y=3^x passes through (0,1) because when x=0, y=3^0-> y = 1. This is basically true for all exponential equations when graphed that look like y=a^x for a>0, a!=1. Now what they want you to do is to graph y=3^x and substitute each of 1.5, .5, and -.25 and see where that point is on the graph. Instead of x substitute in 1.5, or .5 or -.25. This will simply be just a single point for each of 1.5, .5, -.25. You will get (1.5,y1), (.5,y2), and (-.25,y3) where y1~=y2~=y3



The other thing that is common to these exponential equations when graphed is that they are all 'above' the x-axis because y=a^x can never be negative! Where a>0 and a~=1.

Notice that 3^(-.25) is the same as 3^(-1/4) = (1/3)^(1/4). I show you this because it should be clear that y=3^(-.25) will never be negative either. It is impossible for a positive number to be negative no matter what you make the exponent.

Hopefully this has opened a few doors for you.

Math Prof