To find the initial value (y-intercept) \( b \) of the linear function given the rate of change \( m = -47 \) and the point \( (14, 3) \), we can use the slope-intercept form of a linear equation:
\[ y = mx + b \]
We can substitute the given values into the equation. Here, \( x = 14 \), \( y = 3 \), and \( m = -47 \):
\[ 3 = -47(14) + b \]
Now, calculate \( -47(14) \):
\[ -47(14) = -658 \]
Substituting this back into the equation:
\[ 3 = -658 + b \]
Now solve for \( b \):
\[ b = 3 + 658 \]
\[ b = 661 \]
None of the provided options match \( b = 661 \), so it's possible there might be a misunderstanding about the correct data or equations. However, if we re-evaluate the initial question's context and the values given, we can double-check.
Please provide any additional information or context that may help clarify the correct approach.