Question

find the equation of the exponential function represented by the table below:
x | y
0 | 5
1 | 15
2 | 45
3 | 135
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, $x$ is the input, and $y$ is the output.

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 $a=5$, $x=1$, $y=15$ into the formula:
$15 = 5b^1$
Divide both sides by 5: $b = \frac{15}{5}=3$

Step4: Verify $b$ with other values

Check $x=2$: $y=5\times3^2=5\times9=45$, which matches the table.
Check $x=3$: $y=5\times3^3=5\times27=135$, which matches the table.

Answer:

$y = 5(3)^x$