Initial population of a town is 18,691 and it has a doubling time of 15 years. What will the population be in 4 years?
population = 18691 (2)^(4/15)
= 22485.7
or appr 22486
To calculate the future population of a town, we can use the formula for exponential growth:
P(t) = Pā * (1 + r)^(t / T)
Where:
- P(t) represents the future population at time t.
- Pā represents the initial population.
- r represents the growth rate per period.
- t represents the number of periods.
- T represents the doubling time.
In this case, the initial population (Pā) is 18,691, the doubling time (T) is 15 years, and we want to calculate the future population in 4 years (t = 4).
First, we need to determine the growth rate (r) per period using the doubling time. The formula for the growth rate is:
r = ln(2) / T
By substituting the values, we can calculate the growth rate:
r = ln(2) / 15
Next, we can substitute the values into the exponential growth formula to calculate the future population in 4 years:
P(4) = 18,691 * (1 + ln(2) / 15)^(4 / 15)
Calculating this equation will give us the future population of the town in 4 years.