Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 534: 16

$y=0.0951x^{2.827}$

Let $y=ax^b$. Then our equations are: $34=a8^b$ and $9=a5^b$. If we divide the second equation by $5^b$ we get: $9=a5^b\\a=\frac{9}{5^b}\\$. Then $34=\frac{9}{5^b}8^b\\34=9(\frac{8^b}{5^b})\\34=9(\frac{8}{5})^b=9(1.6)^b\\1.6^b=3.777\\\log(1.6)^b=\log(3.777)\\b\log(1.6)=\log(3.777)\\b=\frac{\log(3.777)}{\log(1.6)}\approx 2.827$. Thus $a=\frac{9}{5^{2.827}}\approx0.0951$ Hence, $y=0.0951x^{2.827}$