Exponential Growth

Question

  1. Recall, any exponential function with base greater than one eventually is larger than any positive power function. How big is the exponential function f(x)=1.01^x when it finally overtakes the power function g(x)-x^100?  Write your answer as a power of ten.

Answer 1

As I read the problem:

f(x) = 1.01^x

g(x) = x¹⁰⁰

For what value of x

f(x) > g(x)

1.01^x > x¹⁰⁰

x ln 1.01 > 100 ln x

0.00950 x > 100 ln x

0.0000950 > ln x / x

Is this possible?