Question

x | f(x) or y
0 | 2
1 | 8
2 | 32
3 | 128
4 | 512
what is the y - intercept? a = ______
what is the ratio? b = ______
what is the exponential equation? f(x) = ____________
options:

1. a = 2; b = 6

f(x) = 2 + 6^x

1. a = 2; b = 4

f(x) = 4·2^x

1. a = 2; b = 4

f(x) = 2·4^x

1. a = 2; b = 4

f(x) = 8^x

Explanation:

Step1: Identify Y-intercept (A)

The Y-intercept is $f(0)$. From the table, when $x=0$, $f(0)=2$, so $A=2$.

Step2: Find common ratio (B)

Divide consecutive $f(x)$ values:
$\frac{8}{2}=4$, $\frac{32}{8}=4$, $\frac{128}{32}=4$, $\frac{512}{128}=4$. So $B=4$.

Step3: Build exponential equation

Exponential form is $f(x)=A \cdot B^x$. Substitute $A=2$, $B=4$:
$f(x)=2 \cdot 4^x$

Step4: Match with options

Check which option matches $A=2$, $B=4$, $f(x)=2 \cdot 4^x$.

Answer:

1. A=2; B=4 $f(x)=2 \cdot 4^x$