Question

find the equation of the exponential function represented by the table below:

x	y
0	2
1	8
2	32
3	128

answer attempt 1 out of 2
y = |

Explanation:

Step1: Recall exponential form

The general exponential function is $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor.

Step2: Solve for $a$ using $x=0$

When $x=0$, $y=2$. Substitute into the formula:
$2 = ab^0$
Since $b^0=1$, we get $a=2$.

Step3: Solve for $b$ using $x=1$

Substitute $a=2$, $x=1$, $y=8$ into $y=ab^x$:
$8 = 2b^1$
Divide both sides by 2: $b = \frac{8}{2}=4$

Step4: Verify $b$ with other points

Check $x=2$: $y=2\times4^2=2\times16=32$, which matches the table.
Check $x=3$: $y=2\times4^3=2\times64=128$, which matches the table.

Answer:

$y=2(4)^x$