A logarithmic function of the form \( y=a+b \ln (x+1) \) passes through the points \( (0,-7) \) and \( (908,66) \). Find \( a \) and \( b \), rounding al values to three decimal places, if necessary. Answer Attempt 1 out of 2 \( a=\square b=\square \)

To find the values of \( a \) and \( b \), we can use the given points in the logarithmic function \( y = a + b \ln(x + 1) \). 1. Substitute the point \( (0, -7) \): \[ -7 = a + b \ln(0 + 1) \implies -7 = a + b \cdot 0 \implies a = -7 \] 2. Now substitute the point \( (908, 66) \): \[ 66 = -7 + b \ln(908 + 1) \implies 66 + 7 = b \ln(909) \implies 73 = b \ln(909) \] Thus, we can solve for \( b \): \[ b = \frac{73}{\ln(909)} \] Calculating \( \ln(909) \): \[ \ln(909) \approx 6.511 \] Then, \[ b \approx \frac{73}{6.511} \approx 11.22 \] Finally, rounding to three decimal places, we have: \[ \boxed{a=-7, b=11.220} \]