Final answer:
The estimated membership of the social networking site after 3 months, starting with 5,000 members and increasing by 80% each month, would be 29,160 members. This calculation results from using the formula for compound growth. Hence, the correct membership estimate is not listed among the provided options.
Step-by-step explanation:
To estimate the membership of the social networking site after 3 months with an initial membership of 5,000 and an increase of 80% each month, we need to apply compound growth. The formula to calculate the new number of members is:
Final Membership = Initial Membership × (1 + Growth Rate)^{Number of Periods}
In this case, the growth rate is 80% or 0.8 when expressed as a decimal, and the number of periods is 3 months.
Final Membership = 5,000 × (1 + 0.8)^3
Final Membership = 5,000 × (1.8)^3
Final Membership = 5,000 × 5.832
Final Membership = 29,160
So the estimated membership after 3 months is 29,160, which means that none of the provided options (a) 12,800, (b) 15,000, (c) 18,000, (d) 20,000 are correct.