Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 534: 18

$y=4.456\cdot x^{1.042}$

Let $y=ax^b$. Then our equations are: $14=a3^b$ and $44=a9^b$. If we divide the second equation by the first one we get: $\frac{44}{14}=3^b\\b=\ln_{3}{\frac{44}{14}}\approx1.042$. Then $14=a3^{1.042}\\a=\frac{14}{3^{1.042}}\approx4.456$. Thus $y=4.456\cdot x^{1.042}$