Question

Given real numbers a,b > 1.

Answer 1

Answer:

FALSE

Step-by-step explanation:

Recall that a function f(x) is of exponential order c, if there exists a constant M such that and a real r such that

$|f(x)|\leq Me^{cx}\;(x\geq r)$

Now, take a = 2.5 and b = 2

The functions

$f(x)=(2.5)^x\;g(x)=2^x$

are both exponential of order 1, since  

$\lim_{x \to \infty}\frac{f(x)}{e^x}=\lim_{x \to \infty}\frac{g(x)}{e^x}=0$

but a>b