A town has a population of 50,000. Its rate increases 8% every 6 months. Find the population after 4 years.
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to 92,545
Every 6 months means twice a year. So we have 4 years * twice a year increase = 8 compounding periods.
Our formula for compounding an initial population P at time t is P(t) at a compounding percentage i:
P(t) = P * (1 + i)^t
Since 8% is 0.08 as a decimal and t = 4 *2 = 8, we have:
P(8) = 50000 * (1.08)^8
P(8) = 50000 * 1.85093
P(8) = 92,546.51
Since we can't have a partial person, we round down to 92,545