https://file.aiquickdraw.com/mathbot/file/1726019945506w6qxpi28.jpg

The given equation in the image is \( y = m \cdot 3^x + c \), where \( m \) and \( c \) are integers. One of the points that passes through the curve is \( \left(-2, \frac{61}{9}\right) \).

We can substitute the coordinates of this point into the equation to find the value of \( m \).

The equation is \( y = m \cdot 3^x + c \), and the point is \( (-2, \frac{61}{9}) \), so substituting this into the equation:

\[
\frac{61}{9} = m \cdot 3^{-2} + c
\]

Now, \( 3^{-2} = \frac{1}{9} \), so the equation becomes:

\[
\frac{61}{9} = m \cdot \frac{1}{9} + c
\]

Multiplying through by 9 to eliminate the denominators:

\[
61 = m + 9c
\]

Now, we can use this equation to calculate \( m \) based on the possible integer values of \( c \). Let's proceed to find the possible values of \( m \).The equation simplifies to \( m = 61 - 9c \).

Since \( m \) and \( c \) are both integers, we need to test integer values of \( c \) to find which one yields an \( m \) that matches the choices provided in the question. Let's test values of \( c \) to check for \( m = 1, 2, 0, -1, -2 \).It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can help guide you through the next steps manually:

You have \( m = 61 - 9c \). Now, substitute values of \( c \) and see which one gives a value for \( m \) that matches one of the given options:
- \( c = 0 \) gives \( m = 61 - 9(0) = 61 \)
- \( c = 1 \) gives \( m = 61 - 9(1) = 52 \)
- Continue testing different integer values of \( c \).

Let me know if you want to continue or have questions.

Some related questions to expand understanding:
1. How does the value of \( m \) affect the curve's behavior?
2. What would happen to the graph if the value of \( c \) were changed?
3. What is the significance of the point \( (-2, \frac{61}{9}) \) in solving this problem?
4. How can we graphically interpret \( 3^x \) in exponential functions?
5. How does the constant \( c \) in exponential equations affect the y-intercept?

**Tip:** Always verify solutions by substituting values back into the original equation to ensure accuracy.

Bentuk persamaan kurva di bawah yaitu y = m * 3^x + c, dengan m & c merupakan bilangan bulat. Salah satu titik yang melalui kurva tersebut adalah (-2, 61/9). Tentukan nilai m.

Learn how to determine the value of m in the exponential curve equation y = m * 3^x + c given the point (-2, 61/9). This problem covers exponential functions, point-slope substitution, and integer-based equation solving, suitable for high school students.

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