question\nfind the equation of the exponential function represented by the table below:\n\nanswer attempt 1…

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 $y=ab^x$: $15 = 5b^1$ Rearrange to solve for $b$: $b = \frac{15}{5} = 3$

Step4: Verify $b$ with other points

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:

$y = 5(3)^x$