Given \(y = ab^x\), taking natural logarithms gives \(\ln y = \ln a + x \ln b\).

For the point (1, 3.7):

\(3.7 = \ln a + 1 \cdot \ln b\)

For the point (2.2, 6.46):

\(6.46 = \ln a + 2.2 \cdot \ln b\)

We have two equations:

1. \(3.7 = \ln a + \ln b\)

2. \(6.46 = \ln a + 2.2 \ln b\)

Subtract equation 1 from equation 2:

\(6.46 - 3.7 = (\ln a + 2.2 \ln b) - (\ln a + \ln b)\)

\(2.76 = 1.2 \ln b\)

\(\ln b = \frac{2.76}{1.2} = 2.3\)

\(b = e^{2.3} \approx 9.97\)

Substitute \(\ln b = 2.3\) into equation 1:

\(3.7 = \ln a + 2.3\)

\(\ln a = 3.7 - 2.3 = 1.4\)

\(a = e^{1.4} \approx 4.06\)