To interpret the coefficient in the equation \( C = 18 \times 4^x \), we need to clarify the components of the equation.
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Understanding the Equation:
- \( C \) represents a dependent variable.
- \( 18 \) is a coefficient that multiplies the term \( 4^x \).
- \( 4^x \) represents an exponential growth factor, where \( x \) is an independent variable.
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Role of the Coefficient (18):
- The coefficient \( 18 \) indicates the initial value or the scale factor of the function when \( x = 0 \).
- It affects the overall output value \( C \) but does not change the rate of growth defined by the exponential part \( 4^x \).
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Interpretation of the Coefficient:
- \( 18 \) can be interpreted as the value of \( C \) when \( x = 0\): \[ C = 18 \times 4^0 = 18 \times 1 = 18. \]
- The coefficient indicates that the output value of \( C \) at the base case (when \( x \) is zero) is \( 18 \).
- As \( x \) increases, \( C \) will grow exponentially due to the \( 4^x \) term, but the coefficient \( 18 \) establishes the starting point of this exponential growth.
Conclusion
A correct interpretation of the coefficient \( 18 \) in the equation \( C = 18 \times 4^x \) is that it represents the initial or baseline value of \( C \) when \( x = 0 \). It scales the output of the exponential function \( 4^x \) and determines the magnitude of \( C \) at that point.
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