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The graph shown is on a semi-logarithmic scale, where the \( y \)-axis represents \(\log(y)\) and the \( x \)-axis is linear. This setup typically means that the plotted relationship is exponential in nature.

### Steps to Find the Equation
1. **Identify the Equation Format**: On a semi-log plot, a straight line indicates an exponential function. Since the y-axis is in terms of \(\log(y)\), the equation we expect for \( y(x) \) is:
   \[
   y = a \cdot e^{bx}
   \]
   where \( a \) is the initial value, and \( b \) is the rate of growth (or decay if \( b < 0 \)).

2. **Analyze the Line**: Since the graph of \(\log(y)\) is linear with respect to \( x \), we can model \(\log(y) = bx + \log(a)\).

3. **Determine Slope and Intercept**:
   - By examining two points on the line, determine the slope, \( b \).
   - Identify the intercept on the \(\log(y)\)-axis, which gives \(\log(a)\).

4. **Convert to Exponential Form**: After calculating \( a \) and \( b \), use these values in the form \( y = a \cdot e^{bx} \).

Let me know if you’d like help finding specific points on the line for a more detailed calculation!

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### Questions to Consider:
1. How does a semi-logarithmic scale help in identifying exponential relationships?
2. Why does a straight line on a semi-log plot represent exponential growth or decay?
3. What role does the slope of the line on a \(\log(y)\) vs. \(x\) plot play in determining the rate of growth?
4. How would the equation change if the line had a negative slope?
5. What are some real-world applications of exponential trends represented on semi-logarithmic graphs?

**Tip:** In semi-logarithmic plots, remember that the slope corresponds to the exponent's coefficient in the exponential equation.

Find an equation for the graph shown on a semi-log scale, where the y-axis represents log(y) and the x-axis is linear.

Learn how to find the equation of an exponential function on a semi-log scale. This guide covers identifying exponential relationships and interpreting linear trends on logarithmic graphs, ideal for high school math students.

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