which of the following is a graph for f(x)=e^0.2x?
which of the following is a graph for f(x)=e^0.2x?
Answer
Explanation:
Step1: Analyze the function type
The function $f(x)=e^{0.2x}$ is an exponential - growth function of the form $y = a\cdot e^{bx}$ where $a = 1$ and $b=0.2>0$.
Step2: Determine key characteristics
For an exponential - growth function $y = e^{bx}$ with $b>0$, when $x = 0$, $y=e^{0}=1$. As $x$ increases, $y$ increases exponentially, and as $x$ decreases towards negative infinity, $y$ approaches $0$ but never reaches it.
Answer:
The fourth graph (the one that starts close to the $x$ - axis for negative $x$ - values, passes through the point $(0,1)$ and increases as $x$ increases).