which equation represents an exponential function with an initial value of 500?\n$f(x)=100(5)^x$\n$f(x)=100(x…

Explanation:

Step1: Recall exponential - function form

The general form of an exponential function is $f(x)=a\cdot b^{x}$, where $a$ is the initial value and $b>0,b\neq1$.

Step2: Check each option

• For $f(x)=100(5)^{x}$, the initial value $a = 100$.
• For $f(x)=100(x)^{5}$, this is not an exponential function in the form $a\cdot b^{x}$.
• For $f(x)=500(2)^{x}$, it is in the form $a\cdot b^{x}$ with $a = 500$ (the initial - value) and $b = 2$.
• For $f(x)=500(x)^{2}$, this is a quadratic - like function, not an exponential function in the form $a\cdot b^{x}$.

Answer:

$f(x)=500(2)^{x}$