Question

what is the y-intercept? a=_______ what is the ratio? b=______ what is the exponential equation? f(x)=___________ a=2; b=3 f(x)=6^x a=2; b=3 f(x)=2·3^x a=1; b=3 f(x)=3^x a=3; b=2 f(x)=3·2^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 $(0,3)$, so $A=3$.

Step2: Determine growth ratio (B)

Use a second point on the graph. When $x=1$, $f(1)=6$. Substitute $A=3$, $x=1$, $f(1)=6$ into $f(x)=A \cdot B^x$:
$6 = 3 \cdot B^1$
Solve for $B$: $B=\frac{6}{3}=2$

Step3: Write exponential equation

Substitute $A=3$ and $B=2$ into the standard form: $f(x)=3 \cdot 2^x$

Answer:

A=3; B=2 $f(x)=3 \cdot 2^x$ (matches the blue option)