Question

Which equation represents exponential growth?

A. f(x)=2(3)^x
B. f(x)=3(0.11)^x
C. f(x)=2(1/2)^x
D. f(x)=5(1/6^x)

Answer 1

Growth means a base for exponentiation bigger than 1  (in absolute value), otherwise it's decay.

Only the first choice has a base biggerthan 1.  The last choice is equivalent to $f(x)=5 ( \frac 1 6)^x$ so has a base less than 1.

Answer: A

Answer 2

Note how answer A has the form  (constant)(constant greater than 1)^exponent.  This is how you recognize expo growth.  The other 3 answer choices are disqualified because their bases {0.11, 1/2, 1/6} are fractions between 0 and 1.

The correct answer is A.