Question

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

x	y
0	5
1	10
2	20
3	40

answer attempt 1 out of 3
y = | submit answer

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 $x=0$, $y=5$. Substitute into the formula:
$5 = ab^0$
Since $b^0=1$, we get $a=5$.

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

Substitute $a=5$, $x=1$, $y=10$ into $y=ab^x$:
$10 = 5b^1$
Solve for $b$: $b = \frac{10}{5}=2$

Step4: Write the final equation

Substitute $a=5$ and $b=2$ into $y=ab^x$.

Answer:

$y=5(2)^x$