To find the best exponential equation for the given points, we need to model the data using an exponential function of the form:

$y = a \cdot e^{bx}$ where:

• $y$ is the dependent variable (output),
• $x$ is the independent variable (input),
• $a$ and $b$ are constants to be determined.

Steps to find the equation:

1. Use the points $(x_1, y_1) = (24, 274524)$, $(x_2, y_2) = (25, 276954)$, and $(x_3, y_3) = (26, 292476)$.
2. Fit these points to the general form $y = a \cdot e^{bx}$, by solving for $a$ and $b$.
3. This can be done by transforming the equation into a linear form using natural logarithms and applying linear regression to determine $a$ and $b$.

I'll run through these calculations now to find the best fit exponential equation.

Give me a moment to calculate this.The best-fit exponential equation for the given points is:

$y = 125867.17 \cdot e^{0.03216x}$

Where:

• $a = 125867.17$
• $b = 0.03216$

This equation models the relationship between $x$ and $y$ based on the provided data.

Would you like more details on how this was derived, or do you have any further questions?

Here are 5 questions you might consider next:

1. How do logarithms help linearize an exponential equation?
2. What is the significance of the base $e$ in the exponential equation?
3. How can you determine if the exponential model fits well to the data points?
4. Can you apply this model to predict future values (e.g., $x = 27$)?
5. What is the interpretation of the constants $a$ and $b$ in the context of this model?

Tip: When fitting data to an exponential model, checking the residuals (the difference between observed and predicted values) can help assess the model's accuracy.