identifying exponential decay functions\nwhich is an exponential decay function?\n1. $f(x)=0.2\\left(\\frac{5…

identifying exponential decay functions\nwhich is an exponential decay function?\n1. $f(x)=0.2\\left(\\frac{5}{3}\\right)^x$\n2. $f(x)=10^x$\n3. $f(x)=-3.1^x$\n4. $f(x)=-2(0.7)^x$

identifying exponential decay functions\nwhich is an exponential decay function?\n1. $f(x)=0.2\\left(\\frac{5}{3}\\right)^x$\n2. $f(x)=10^x$\n3. $f(x)=-3.1^x$\n4. $f(x)=-2(0.7)^x$

Answer

Explanation:

Step1: Recall decay function rule

An exponential decay function has the form $f(x)=a(b)^x$, where $0<b<1$ and $a\neq0$.

Step2: Check each function's base

  1. $f(x)=0.2\left(\frac{5}{3}\right)^x$: $\frac{5}{3}\approx1.67>1$ (growth)
  2. $f(x)=10^x$: $10>1$ (growth)
  3. $f(x)=-3.1^x$: $3.1>1$ (growth, negative $a$ flips graph)
  4. $f(x)=-2(0.7)^x$: $0<0.7<1$ (decay, negative $a$ flips graph)

Answer:

$f(x) = -2(0.7)^x$