Question
Which function is increasing?
A. F(x)= (1/15)^x
B. f(x) = (0.5) ^x
C. F(x)= (1/5)^x
D. f(x)=5^x
A. F(x)= (1/15)^x
B. f(x) = (0.5) ^x
C. F(x)= (1/5)^x
D. f(x)=5^x
Answers
Answered by
GPT-4o mini
To determine which function is increasing, we can analyze the base of the exponent in each function.
- A. \( F(x) = \left(\frac{1}{15}\right)^x \): This function has a base less than 1. As \( x \) increases, \( F(x) \) decreases.
- B. \( f(x) = (0.5)^x \): Similar to A, this function has a base less than 1. As \( x \) increases, \( f(x) \) decreases.
- C. \( F(x) = \left(\frac{1}{5}\right)^x \): Again, this has a base less than 1. So, as \( x \) increases, \( F(x) \) decreases.
- D. \( f(x) = 5^x \): This function has a base greater than 1. As \( x \) increases, \( f(x) \) increases.
Thus, the increasing function is:
**D. \( f(x) = 5^x \)**.
- A. \( F(x) = \left(\frac{1}{15}\right)^x \): This function has a base less than 1. As \( x \) increases, \( F(x) \) decreases.
- B. \( f(x) = (0.5)^x \): Similar to A, this function has a base less than 1. As \( x \) increases, \( f(x) \) decreases.
- C. \( F(x) = \left(\frac{1}{5}\right)^x \): Again, this has a base less than 1. So, as \( x \) increases, \( F(x) \) decreases.
- D. \( f(x) = 5^x \): This function has a base greater than 1. As \( x \) increases, \( f(x) \) increases.
Thus, the increasing function is:
**D. \( f(x) = 5^x \)**.