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
[tex]|f(x)|\leq Me^{cx}\;(x\geq r)[/tex]
Now, take a = 2.5 and b = 2
The functions
[tex]f(x)=(2.5)^x\;g(x)=2^x[/tex]
are both exponential of order 1, since
[tex]\lim_{x \to \infty}\frac{f(x)}{e^x}=\lim_{x \to \infty}\frac{g(x)}{e^x}=0[/tex]
but a>b
