Which of the following options results in a graph that shows exponential growth?

A.f(X)= 0.4(3)X
B.f(X)= 3(0.5)X
C.f(X)= 0.8(0.9)X
D.f(X)= 0.9(5)-X

Which of the following options results in a graph that shows exponential growth?

A.f(X)= 0.4(3)^X
B.f(X)= 3(0.5)^X
C.f(X)= 0.8(0.9)^X
D.f(X)= 0.9(5)^-X

To determine which of the given options represents exponential growth, let's analyze each function:

A. f(x) = 0.4(3)^x
B. f(x) = 3(0.5)^x
C. f(x) = 0.8(0.9)^x
D. f(x) = 0.9(5)^(-x)

Exponential growth occurs when the base of the exponential term is greater than 1. In other words, for exponential growth, the value inside the parentheses should be greater than 1.

Analyzing the options:

A. In this case, the base is 3, which is greater than 1. Therefore, option A represents exponential growth.
B. In this case, the base is 0.5, which is less than 1. Therefore, option B does not represent exponential growth.
C. In this case, the base is 0.9, which is less than 1. Therefore, option C does not represent exponential growth.
D. In this case, the base is 5 raised to the power of -x, which is less than 1. Therefore, option D does not represent exponential growth.

Therefore, the option that results in a graph showing exponential growth is A. f(x) = 0.4(3)^x.

To determine which option represents a graph showing exponential growth, we need to examine the equations and look for the characteristics of exponential functions.

Exponential growth occurs when the base of the exponential term is greater than 1. In other words, the value inside the parentheses must be larger than 1.

Let's evaluate each option:

A) f(X)= 0.4(3)X
The base of the exponential term is 3. This means the equation represents exponential growth.

B) f(X)= 3(0.5)X
The base of the exponential term is 0.5. This is less than 1, so it does not represent exponential growth.

C) f(X)= 0.8(0.9)X
The base of the exponential term is 0.9. This is less than 1, so it does not represent exponential growth.

D) f(X)= 0.9(5)-X
In this option, the variable X is in the exponent, so it is an exponential function. However, the base of the exponential term is 0.9 (since 5-X = 5-1 = 4), which is less than 1 and does not represent exponential growth.

Therefore, the option that results in a graph showing exponential growth is option A) f(X)= 0.4(3)X.

Which of the following options results in a graph that shows exponential growth?