Let $A(t)$ represent your bank account balance, in dollars, after $t$ years. Suppose you start with $\$ 40,000$ in the account. The account earns $7 \%$ interest compounded continuously, and you contribute $\$ 10,000$ per year. A. Write the differential equation that models this situation. \[ \frac{d A}{d t}= \] B. The initial condition is: \[ A(0)= \]

Step 1 ：Translate the problem into a mathematical model. The problem states that the bank account balance, represented by A(t), grows at a rate of 7% per year, compounded continuously, and an additional $10,000 is added to the account each year. This can be represented by the differential equation \(\frac{d A}{d t}= 0.07A(t) + 10000\).

Step 2 ：Identify the initial condition. The problem states that the initial bank account balance is $40,000. This can be represented as \(A(0)= 40000\).

Step 3 ：Combine the differential equation and the initial condition to form the complete mathematical model of the problem. The differential equation is \(\frac{d A}{d t}= 0.07A(t) + 10000\) and the initial condition is \(A(0)= 40000\).