Question

what is the y - intercept? a = -------
what is the ratio? b = -------
what is the exponential equation? f(x) = -------
a=1; b=3 $f(x)=3^x$
a=3; b=2 $f(x)=3\cdot2^x$
a=2; b=3 $f(x)=6^x$
a=2; b=3 $f(x)=2\cdot3^x$

Explanation:

Step1: Identify Y-intercept (A)

The Y-intercept of an exponential function $f(x)=A \cdot B^x$ is the value when $x=0$. For $x=0$, $f(0)=A \cdot B^0 = A$. From the graph, the curve crosses the y-axis at $(0,1)$, so $A=1$.

Step2: Identify growth ratio (B)

For an exponential function, the ratio $B$ is the factor by which $f(x)$ increases when $x$ increases by 1. When $x=1$, $f(1)=3^1=3$, so the ratio between $f(1)$ and $f(0)$ is $\frac{3}{1}=3$, so $B=3$.

Step3: Form the exponential equation

Substitute $A=1$ and $B=3$ into the standard exponential form $f(x)=A \cdot B^x$, giving $f(x)=3^x$.

Answer:

A=1; B=3 $f(x)=3^x$