Finding best fitted value for power function. please help!

Question

I need to find: 1. the best fitted value for $a$ in the power function 2. the best fitted value for $b$ in the power function

Data given:

I know that $b=bi$ and $a=e^{bo}$ --> my question is how to find $bo$ and $bi$, since $log$ equations are given? can I use this equation to find bi for power function:

$Exy- (Ex)(Ey)$ -------- $n$

---

$Ex2-(Ex)2$ ------- $n$

Where $E$ stands for addition.

Thank you so much!

Answer 1

So $y = a_0x^{a_1}$ take the logarithm $log(y)=log(a_0)+a_1*log(x)$. This is a linear regression, use the standard formulas. $y = a*exp(b*x)$ take the logarithm $log(y)=log(a)+b*x$ This is also a simple linear regression, where you can use the standard formulas.