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Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several...

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tgl223 | Student, College Freshman | eNoter

Posted October 21, 2010 at 1:33 AM via web

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Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles.

There should be a smaller x value and a larger x value.

I found that the smaller x value is (1.8,17.1).

I cannot find the larger x value.

"Find all points of intersection of the graphs correct to one decimal place."

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kjcdb8er | Teacher | (Level 1) Associate Educator

Posted October 21, 2010 at 7:26 AM (Answer #1)

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You can see a graph of the two functions here:

http://www.wolframalpha.com/input/?i=x^5+%3D+5^+x+

As you can see, the primary difference is that the latter grows exponentially, while the former grows in polynomial time.

It should also be apparent that there are two points of intersection.

Those points are found by solving the equation,

x^5 = 5^x

Looking at this equation, what happens if you substitute x = 5 ?

So, your two points of intersection are:

(1.8,17.1) , (5, 5^5)

 

 

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