Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Quiz for Lessons 7.6-7.7 - Page 536: 13

$y=1.316\cdot x^{1.302}$

Let $y=ax^b$. Then our equations are: $8=a4^b$ and $23=a9^b$. If we divide the second equation by the first one we get: $2.875=2.25^b\\b=\ln_{2.25}{2.875}\approx1.302$. Then $8=a4^{1.302}\\a=\frac{8}{4^{1.302}}\approx1.316$. Thus $y=1.316\cdot x^{1.302}$