f(x)=2*(1/3)^x

Question

State wether the function is exponentional Growth or Decay, and describe its end behavior useing limits.  

f(x)=2*(1/3)^x

Answer 1

This is exponential decay because the term with the exponent (1/3) is positive and less than 1. 

The graph passes through the point (0,2). It rises to the left and falls to the right.

End behavior:

as x approaches +infinity, y approaches 0. (The limit as x ---->+infinity = 0)

as x approaches -infinity, y approaches +infinity. (The limit as x ----> -infinity = +infinity.

In other terms, the domain is all real numbers, and the range is y>0.

Answer 2

as x increases (1/3)^x decreases, it's decay not growth

(1/3)^1 = 1/3

(1/3)^2 = 1/9

(1/3)^3 = 1/27

...

(1/3)^50000 = nearly zero

it's decaying