Question

for the function f(x)=a(b)^x, where 0 < b < 1, what value does the function's output approach as x gets very large?

Answer 1

The value that the function's output approaches as x gets very large is 0.

Step-by-step explanation:

• The function f(x) = a(b)^x, where 0 < b < 1, approaches 0 as x gets very large.
• To understand why, let's look at the exponential function a(b)^x. When the base b is between 0 and 1, the function gets smaller as x gets larger.
• This is because as x increases, the power to which b is raised becomes larger, resulting in a smaller value overall.

For example, let's take b = 0.5.

• When x = 0, the function is f(0) = a(0.5)^0 = a(1) = a.
• As x increases, the value of (0.5)^x decreases.
• So as x approaches infinity, the value of f(x) approaches 0.