question 10 of 10\nwhich function is increasing?\na. $f(x) = \\left(\\frac{1}{15}\\right)^x$\nb. $f(x) =…

question 10 of 10\nwhich function is increasing?\na. $f(x) = \\left(\\frac{1}{15}\\right)^x$\nb. $f(x) = (0.5)^x$\nc. $f(x) = \\left(\\frac{1}{5}\\right)^x$\nd. $f(x) = 5^x$

question 10 of 10\nwhich function is increasing?\na. $f(x) = \\left(\\frac{1}{15}\\right)^x$\nb. $f(x) = (0.5)^x$\nc. $f(x) = \\left(\\frac{1}{5}\\right)^x$\nd. $f(x) = 5^x$

Answer

Explanation:

Step1: Recall exponential function rules

An exponential function has the form $f(x)=a^x$. If $a>1$, the function is increasing; if $0<a<1$, it is decreasing.

Step2: Analyze each option

  • Option A: $a=\frac{1}{15}\approx0.07$, $0<0.07<1$, decreasing.
  • Option B: $a=0.5$, $0<0.5<1$, decreasing.
  • Option C: $a=\frac{1}{5}=0.2$, $0<0.2<1$, decreasing.
  • Option D: $a=5$, $5>1$, increasing.

Answer:

D. $f(x) = 5^{x}$