Do you want to solve for x and y?
What is the objective?
6.74
7.69
5.92
6.68
i listed the unit prices in order and the lowest unit price is for the 10 oz one
your missing information
how often is it compounded? monthly,yearly, annually, daily?
You can use the root test here. The series will converge if
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3C1)
You have
![L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}](https://tex.z-dn.net/?f=L%3D%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cfrac%7B%284-x%29%5En%7D%7B4%5En%2B9%5En%7D%7D%3D%7C4-x%7C%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D)
Notice that
![\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B4%5En%2B9%5En%7D%7D%3D%5Cdfrac1%7B%5Csqrt%5Bn%5D%7B9%5En%7D%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D%3D%5Cdfrac1%7B9%5Csqrt%5Bn%5D%7B1%2B%5Cleft%28%5Cfrac49%5Cright%29%5En%7D%7D)
so as

, you have

, which means you end up with

This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of

so that

is the ROC. You get