Question

Let f(x)=4^(x). Does the function represent growth or decay

Answer 1

By looking at the base of the exponential function, the function f(x) = 4ˣ represents growth.

Step-by-step explanation:

To determine whether the function f(x) = 4ˣ represents growth or decay, you can look at the base of the exponential function, which is 4 in this case.

In general, for an exponential function f(x) = aˣ:

1. If the base a is greater than 1, the function represents exponential growth. This is because as x increases, the value of a^x gets larger, indicating the function is increasing.

2. If the base a is between 0 and 1 (0 < a < 1), the function represents exponential decay. This is because as x increases, the value of a^x gets smaller, indicating the function is decreasing.

Given the function f(x) = 4ˣ, the base is 4, which is clearly greater than 1. Thus, the function represents exponential growth. As x increases, the function f(x) will increase rapidly due to the nature of exponential growth.