which is the graph of $f(x)=100(0.7)^x$?
which is the graph of $f(x)=100(0.7)^x$?
Answer
Explanation:
Step1: Analyze the exponential - function form
The general form of an exponential function is $y = a\cdot b^{x}$, where $a = 100$ and $b=0.7$. Since $0 < b<1$, the function is a decaying exponential function. When $x = 0$, $y=a\cdot b^{0}=a$. So when $x = 0$, $y = 100(0.7)^{0}=100$.
Step2: Calculate the value at $x = 2$
Substitute $x = 2$ into the function $y=100(0.7)^{x}$. We get $y = 100\times(0.7)^{2}=100\times0.49 = 49$.
Answer:
The first graph (the one with points $(0,100)$ and $(2,49)$) is the graph of $f(x)=100(0.7)^{x}$.