Questions: Find the equation of the exponential function represented by the table below: x y 0 1 1 4 2 16 3 64

Transcript text: Find the equation of the exponential function represented by the table below: \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 0 & 1 \\ \hline 1 & 4 \\ \hline 2 & 16 \\ \hline 3 & 64 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the general form of the exponential function

The general form of an exponential function is: \[ y = a \cdot b^x \] where:

$a$ is the initial value (when $x = 0$),
$b$ is the base (the growth factor).

Step 2: Determine the initial value $a$

From the table, when $x = 0$, $y = 1$. Substituting into the general form: \[ 1 = a \cdot b^0 \] Since $b^0 = 1$, this simplifies to: \[ a = 1 \]

Step 3: Determine the base $b$

Using the value $x = 1$ and $y = 4$ from the table, substitute into the general form: \[ 4 = 1 \cdot b^1 \] This simplifies to: \[ b = 4 \]

Step 4: Write the equation of the exponential function

Substitute $a = 1$ and $b = 4$ into the general form: \[ y = 1 \cdot 4^x \] Simplifying: \[ y = 4^x \]

Final Answer

The equation of the exponential function is: \[ \boxed{y = 4^x} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!