Question

Which of the following exponential functions is an increasing function calculator?

A) f(x) = eˣ
B) g(x) = 2ˣ
C) h(x) = 1/(3ˣ)
D) k(x) = 10⁻ˣ

Answer 1

The functions A) f(x) = e^x and B) g(x) = 2^x are increasing functions because as x increases, their outputs increase. In contrast, functions C) h(x) = 1/(3^x) and D) k(x) = 10^(-x) are decreasing functions. The correct answer is option B

Step-by-step explanation:

An increasing exponential function is characterized by a base greater than 1. Among the provided options, option (B) g(x) = 2ˣ is the correct choice. As x increases, the value of 2 raised to the power of x also increases, resulting in exponential growth. This is because the base, 2, is greater than 1, leading to a continual upward trend in the function's values.

On the contrary, options (A) f(x) = eˣ, (C) h(x) = 1/(3ˣ), and (D) k(x) = 10⁻ˣ involve bases e, 1/3, and 10⁻¹, respectively, all of which are less than 1. These bases result in decreasing exponential functions, as the values diminish as x increases. Therefore, option (B) represents the only increasing exponential function among the given choices.