Question

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

x	y
1	0.8
2	3.2
3	12.8

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: Find $a$ using $x=0$

When $x=0$, $y=0.2$. Substitute into the formula:
$0.2 = ab^0$
Since $b^0=1$, we get $a=0.2$.

Step3: Find $b$ using $x=1$

Substitute $x=1$, $y=0.8$, $a=0.2$ into the formula:
$0.8 = 0.2b^1$
Solve for $b$: $b = \frac{0.8}{0.2} = 4$

Step4: Verify $b$ with other values

Check $x=2$: $y=0.2(4)^2 = 0.2\times16 = 3.2$, which matches the table.
Check $x=3$: $y=0.2(4)^3 = 0.2\times64 = 12.8$, which matches the table.

Answer:

$y=0.2(4)^x$