Answer:
D. ![\left\{\begin{matrix}B=50,000-2,500t \\B=2,000e^{0.05t} \end{matrix}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7DB%3D50%2C000-2%2C500t%20%5C%5CB%3D2%2C000e%5E%7B0.05t%7D%20%5Cend%7Bmatrix%7D%5Cright.)
Step-by-step explanation:
In checking account,
The initial amount = $50,000,
Lisa will be withdrawing funds from her checking account over the course of each year to pay bills at an average rate of $2,500.
Thus, the total amount she withdrawn in t years = 2500t,
Hence, the amount left in her checking account,
B = 50,000 - 2500t
Now, in saving account,
The principal amount = $ 2,000,
The rate of compounding continuously, r = 5% = 0.05,
Thus, the amount left after t years,
![B=Pe^{rt}](https://tex.z-dn.net/?f=B%3DPe%5E%7Brt%7D)
![\implies B=2,000e^{0.05t}](https://tex.z-dn.net/?f=%5Cimplies%20B%3D2%2C000e%5E%7B0.05t%7D)
Hence, the systems of equations can be used to determine how long it will be before the balance in each account is equal,
![\left\{\begin{matrix}B=50,000-2,500t \\B=2,000e^{0.05t} \end{matrix}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Bmatrix%7DB%3D50%2C000-2%2C500t%20%5C%5CB%3D2%2C000e%5E%7B0.05t%7D%20%5Cend%7Bmatrix%7D%5Cright.)
Option 'D' is correct.