Question

Which statement best describes the conditions for f ( x ) = a ( b ) x to be a model for exponential growth?

Answer 1

Exponential functions grow is the base is greater than 1, while you have an exponential decay if the base is between 0 and 1. Finally, exponentials are not defined, as real functions, if the base is negative.

So, the answer is D, b > 1

Answer 2

Answer:

Option D - b>1

Step-by-step explanation:

To find : Which statement best describes the conditions for $f(x)=ab^x$ to be a model for exponential growth?

Solution :

The exponential function is in the form $f(x)=ab^x$

where, a is the initial amount and b is the growth/decay rate factor.

and $a\neq 0,\ b>0,\ b\neq 1$ and x is any real number.

Condition for exponential growth is when b is greater than 1.

i.e. $f(x)=ab^x$ to be a model for exponential growth when b>1.

Therefore, option D is correct.