Question about a mathematical function.

[DeltaIceman]

Hi I'm a calculas student and about every 2 weeks we are given an assignment on matlab. I'm not sure if any of you are familiar with the program. Anyway as I was working my way through the steps on the paper is to graph e^x and 10^x. On my screen I'm shown a graphy unfortunately I'm unable to load it up on to hear. But I was able to estimate 2 intersection points. which were very close to the coordinates (1.118, 3.059) and (-.913, .401) now after getting to this point. The paper I'm working off of states that there must be another solution of x^10= e^x that is larger then the first solution I found. And it wants me to explain why. I know that x^10 blows up from the start to an extremely high number. And I know that e^x starts growing smaller but has a larger base. So is the reason that my teachers are looking for is that while X^10 grows large extremely fast e^x has a larger base and eventually catches up with x^10 and crosses it again.

 

[John Creighto]

Is it 10^x you should be graphing or x^10. Anyway, MATLAB let's you save graphs as images. You can also copy and paste. However, I don't think we'll need to see the plot to answer the question.

 

[Mentallic]

DeltaIceMan you have it spot on. Even though x¹⁰ shoots straight up quickly after x=1, jumping to 1024 at x=2... etc. e^x climbs pretty slowly soon after x=1, but grow exponentially (remember, a^x for a>1 will always grow faster than any polynomial of degree n... eventually )
Try using Newton's method to find the intersection of these graphs at the larger value of x. Don't be surprised by its size, as I know you're probably thinking of much larger values.