Question

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

A. b > 0

B. b < 0

C. 0 < b < 1

D. b > 1

Answer 1

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.

Answer 2

We want to see which statement describes the condition for a function to be a model for exponential growth.

The correct option is D: b > 1.

A exponential growth is a function that grows slower at first and faster as x increases.

The general form is:

f(x) = a*(b)^x

Where a is the initial value, b is the rate of growth, and x is the variable.

If b = 1, then this function is constant.

if 0 < b < 1, then the function decreases as x increases.

if b > 1, the function increases as x increases.

Then we can conclude that the exponential growth needs to have a rate of growth larger than 1, then the correct option is D: b > 1.

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