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: 15

$y=0.022\cdot x^{3.229}$

Let $y=ax^b$. Then our equations are: $4=a5^b$ and $51=a11^b$. If we divide the second equation by the first one we get: $12.75=2.2^b\\b=\ln_{2.2}{12.75}\approx3.229$. Then $4=a5^{3.229}\\a=\frac{4}{5^{3.229}}\approx0.022$. Thus $y=0.022\cdot x^{3.229}$