To solve this problem, we need to integrate the function f(x) = 100e^-x/2 from 0 to 4 as this will give us the total number of condominiums sold in the first 4 weeks.
In more detail:
1. First, we get the function representing the rate of condominiums being sold each week, which is f(x) = 100e^-x/2.
2. Since we're interested in the total number of condominiums sold over a period of 4 weeks, we need to calculate the definite integral of f(x) from 0 to 4.
3. We write down the integral ∫f(x) dx from 0 to 4.
4. By substituting the limits of integration into the function, we compute the definite integral.
5. After calculating the integral, we find the area under the curve which represents the total number of condominiums sold over the 4 weeks.
6. The result comes out as a decimal number. Since it's not practical to sell a fraction of a condominium, we round this number to the nearest integer.
After performing these steps, we find that the real estate office will sell approximately 173 condominiums during the first 4 weeks.