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 y-intercept, $b$ is the growth/decay factor.

Step2: Find $a$ using $x=0$

When $x=0$, $y=5$. Substitute into $y=ab^x$: $5 = ab^0$ Since $b^0=1$, $a=5$.

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

Substitute $a=5$, $x=1$, $y=2.5$ into $y=ab^x$: $2.5 = 5b^1$ Solve for $b$: $b = \frac{2.5}{5} = 0.5 = \frac{1}{2}$

Step4: Write final equation

Substitute $a=5$ and $b=\frac{1}{2}$ into $y=ab^x$.

Answer:

$y = 5\left(\frac{1}{2}\right)^x$