Answer:
Option B.
Step-by-step explanation:
Option A.
f(x) = [tex](0.5)^{x}[/tex]
Derivative of the given function,
f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]
= [tex](0.5)^x[\text{ln}(0.5)][/tex]
= [tex]-(0.693)(0.5)^{x}[/tex]
Since derivative of the function is negative, the given function is decreasing.
Option B. f(x) = [tex]5^x[/tex]
f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]
= [tex](5)^x[\text{ln}(5)][/tex]
= [tex]1.609(5)^x[/tex]
Since derivative is positive, given function is increasing.
Option C. f(x) = [tex](\frac{1}{5})^x[/tex]
f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]
= [tex]\frac{d}{dx}(5)^{(-x)}[/tex]
= [tex]-5^{-x}.\text{ln}(5)[/tex]
Since derivative is negative, given function is decreasing.
Option D. f(x) = [tex](\frac{1}{15})^x[/tex]
f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]
= [tex]-2.708(15)^{-x}[/tex]
Since derivative is negative, given function is decreasing.
Option (B) is the answer.
