To find an exponential graph and equation that fits the given points, we are looking for an equation of the form:

$y = a \cdot b^x$

Where:

• $y$ is the output (dependent variable),
• $x$ is the input (independent variable),
• $a$ is the initial value (when $x = 0$),
• $b$ is the base or growth factor.

Given Points:

• (24, 274524)
• (25, 276954)
• (26, 292476)

Step 1: Set up the system of equations

Using the exponential equation $y = a \cdot b^x$, we can substitute the points into the equation to form a system of equations. For each point, we get:

1. $274524 = a \cdot b^{24}$
2. $276954 = a \cdot b^{25}$
3. $292476 = a \cdot b^{26}$

Step 2: Divide equations to eliminate $a$

To solve for $b$, we can divide the second equation by the first equation and the third equation by the second equation.

$\frac{276954}{274524} = \frac{a \cdot b^{25}}{a \cdot b^{24}} = b$ $b = \frac{276954}{274524} \approx 1.00885$

Now, divide the third equation by the second:

$\frac{292476}{276954} = \frac{a \cdot b^{26}}{a \cdot b^{25}} = b$ [ b = \frac{292476}{276954} \approx