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: 14

$y=4.406\cdot x^{0.912}$

Let $y=ax^b$. Then our equations are: $12=a3^b$ and $36=a10^b$. If we divide the second equation by the first one we get: $3=(\frac{10}{3})^b\\b=\ln_{\frac{10}{3}}{3}\approx0.912$. Then $12=a3^{0.912}\\a=\frac{12}{3^{0.912}}\approx4.406$. Thus $y=4.406\cdot x^{0.912}$