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

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 $x=0$, $y=0.01$. Substitute into the formula: $0.01 = ab^0$ Since $b^0=1$, we get $a=0.01$.

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

When $x=1$, $y=0.04$, and $a=0.01$. Substitute into the formula: $0.04 = 0.01b^1$ Solve for $b$: $b = \frac{0.04}{0.01} = 4$

Step4: Verify $b$ with other points

Check $x=2$: $y=0.01(4)^2 = 0.01(16)=0.16$, which matches the table. Check $x=3$: $y=0.01(4)^3 = 0.01(64)=0.64$, which matches the table.

Answer:

$y = 0.01(4)^x$