Question

Which is an exponential growth function f(x)=6(0.25)x f(x)=0.25(5.25)x

Answer 1

Answer:

The correct answer option is B. $f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x$.

Step-by-step explanation:

If the numbers are positive along with the base of the exponent which must be greater than 1, then it an exponential growth function.

1. $f(x)=6(0.25)^x$:

Here the numbers are positive but the base of the exponent is 0.25 which is less than 1 so it is not an exponential growth function.

2. $f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x$:

Positive numbers with base of the exponent greater than 1, therefore it is an exponential growth function.

Answer 2

Answer: Second Option

$f(x)=0.25(5.25)^x$

Step-by-step explanation:

The exponential growth functions have the following form:

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

Where a is the main coefficient, b is the base and x is the exponent.

For this type of functions the base b must always be greater than 1. Otherwise it would be an exponential decay function

Among the options given, the only function whose base is greater than 1 is the second option:

$f(x)=0.25(5.25)^x$