Question

x | f(x)=y
-1 | 4/3
0 | 4
1 | 12
2 | 36
3 | 108
what is the y-intercept? a=________
what is the ration? b=________
what is the exponential equation? f(x)=________
a=4/3 ; b=4
f(x) = (4/3)·4^x
a=4; b=3
f(x) = 4·3^x (with a missing character)
a=4/3; b=3
f(x) = (4/3)·3^x
a=4; b=8
f(x) = 4·8^x

Explanation:

Step1: Find y-intercept (A)

The y-intercept is the value of $f(x)$ when $x=0$. From the table, when $x=0$, $f(x)=4$, so $A=4$.

Step2: Find the ratio (B)

The ratio is the factor between consecutive $f(x)$ values. Calculate $\frac{12}{4}=3$, $\frac{36}{12}=3$, $\frac{108}{36}=3$, so $B=3$.

Step3: Form exponential equation

The standard form of an exponential function is $f(x)=A \cdot B^x$. Substitute $A=4$ and $B=3$, so $f(x)=4 \cdot 3^x$.

Answer:

A=4; B=3
$f(x)=4 \cdot 3^x$
(matches the purple option)