# exponents intersections

• Jan 26th 2010, 01:21 PM
ryan18
exponents intersections
Could someone explain how to do this?

Compare the functions given below by graphing both functions in several viewing rectangles. For what values of x does the graph of g finally surpass the graph of f ? (Give your answer correct to 1 decimal place.)
f(x) = x10
g(x) = ex
• Jan 26th 2010, 01:35 PM
e^(i*pi)
Quote:

Originally Posted by ryan18
Could someone explain how to do this?

Compare the functions given below by graphing both functions in several viewing rectangles. For what values of x does the graph of g finally surpass the graph of f ? (Give your answer correct to 1 decimal place.)
f(x) = x10
g(x) = ex

Do you mean

\$\displaystyle f(x) = x^{10}\$
\$\displaystyle g(x) = e^x\$

Find the point of intersection by setting the two equal

As the question says there is no algebraic way to solve so get the calculator out. To make this easier to view I will take the natural log and then plot.

\$\displaystyle x^{10} = e^x\$

\$\displaystyle 10\,ln(x) = x\$

And on the graph they cross at roughly \$\displaystyle (1.116, e^{1.116})\$ so this will be the value
• Jan 26th 2010, 01:43 PM
ryan18
How did you get 1.116?
Is the only way to just graph it out and have the calculator/program tell you the points?
• Jan 26th 2010, 01:50 PM
e^(i*pi)
Quote:

Originally Posted by ryan18
How did you get 1.116?
Is the only way to just graph it out and have the calculator/program tell you the points?

Yeah that's what it's asking you to do. I forgot to attach the graph to the last post so I'll stick it on this one. Remember the actual y co-ordinate will be \$\displaystyle e^{1.116}\$ as I used the natural log to make graphing easier.
• Jan 26th 2010, 01:52 PM
ryan18
Awesome, I should probably get that program. Thanks alot!
• Jan 26th 2010, 01:53 PM
e^(i*pi)
Quote:

Originally Posted by ryan18
Awesome, I should probably get that program. Thanks alot!

Unless you're running Linux I'd suggest searching for a different one (Wink)
• Jan 26th 2010, 02:03 PM
ryan18
So you have to put the answer in terms of x > ____

I put in when x is greater than 1.116, and then I saw the (Give your answer correct to 1 decimal place.) so I tried 1.1 and that still didnt work...?