hi can you please to the best of your ability, find an exponential graph and equation for these points please:

24, 274524

25, 276954
26,292476

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

hi can you please to the best of your ability, find an exponential graph and equation for these points please: 24, 274524; 25, 276954; 26, 292476

Find the exponential equation for the points (24, 274524), (25, 276954), and (26, 292476). Learn the process of setting up exponential equations, dividing to eliminate variables, and solving for growth factors. Ideal for students in Grades 10-12 studying exponential functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation