what is the growth factor of the exponential function represented by the table?\n0.2\n0.1\n5\n20

Explanation:

Step1: Recall exponential - function form

An exponential function is of the form $y = a\cdot b^{x}$, where $b$ is the growth factor. When $x = 0$, $y=a$. From the table, when $x = 0$, $f(x)=0.1$, so $a = 0.1$.

Step2: Use another point to find $b$

Let's use the point $(1,0.5)$. Substitute $x = 1$, $y = 0.5$ and $a=0.1$ into $y=a\cdot b^{x}$. We get $0.5=0.1\cdot b^{1}$.

Step3: Solve for $b$

Divide both sides of the equation $0.5 = 0.1b$ by $0.1$. So, $b=\frac{0.5}{0.1}=5$.

Answer:

5