Question

Compare the rates of growth of the functions correct to one decimal place. x^3 and 3^x

Answer 1

exponential function's grow at a faster rate than polynomials.

Answer 2

right :) The problem wants the point of intersection for the "smaller x value" and the "larger x value". I figured out how to do the larger, but I don't know how to get the smaller. the larger coordinate is (3,3^3)

Answer 3

I'm not sure what you're asking. Are you saying that you are looking for point(s) of intersection?

Answer 4

Yes I am :) I guess it wants the lowest point that the graphs intersect

Answer 5

who said there is a point less than 3?

Answer 6

and what does that have to do with rates of growth?

Answer 7

I have no idea... Calculus "exponential functions" section. Half my homework doesn't make sense...

Answer 8

I don't believe there is such a point less than 3.

Answer 9

But why would the point of intersection have a connection with rates of growth?

Answer 10

Compare the rates of growth of the functions f(x) = x^3 and g(x) = 3^x by graphing both functions in several viewing rectangles. Find all points of intersection of the graphs correct to one decimal place. I don't

Answer 11

OK. so there are two separate questions. And not necessarily any direct relationship between the two. Other than the fact that with small values of x, 3^x and x^3 are close in function values; and as x runs to infinity, 3^x will outrun x^3.

Answer 12

And that is the reason why the two parts are in the same question...to have students realize that for small values of x...a polynomial may be larger than an exponential, but for x----> infinity, the exponential will outrun the polynomial.

Answer 13

Yeah, that makes sense. Thank you! :) Just gotta get numbers though. I hate online math homework...

Answer 14

A typical example would be x^50 and 2^x....now, x^50 is way higher in value than 2^x for the first large number of integers, but as x---> infinity, the little guy called 2^x outrund x^50. fascinating!