# Chapter 7 Exponential and Logarithmic Functions - 7.7 Write and Apply Exponential and Power Functions - 7.7 Exercises - Skill Practice - Page 534: 22

$y=1.924\cdot x^{0.844}$

#### Work Step by Step

Let $y=ax^b$. Then our equations are: $5=a3.1^b$ and $9.7=a6.8^b$. If we divide the second equation by the first one we get: $1.94=(\frac{6.8}{3.1})^b\\b=\ln_{\frac{6.8}{3.1}}1.94\approx0.844$. Then $5=a3.1^{0.844}\\a=\frac{5}{3.1^{0.844}}\approx1.924$. Thus $y=1.924\cdot x^{0.844}$

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