anytown, usa has a population of 323,000 in 1996. the growth rate is 8.4%
Determine the population of anytown in 2013
determine the year in which the population of anytown will double
To determine the population of Anytown in 2013, we first need to calculate the number of years between 1996 and 2013:
2013 - 1996 = 17 years
Next, we calculate the population of Anytown in 2013 using the growth rate of 8.4% per year:
Population in 2013 = 323,000 * (1 + 0.084)^17
Population in 2013 = 323,000 * 3.349721
Population in 2013 = 1,081,377
Therefore, the population of Anytown in 2013 is 1,081,377.
To determine the year in which the population of Anytown will double, we need to use the formula for exponential growth:
P(t) = P(0) * (1 + r)^t
Where:
P(t) = population at time t
P(0) = initial population
r = growth rate
t = number of years
In this case, we want to find the year in which the population will double, so we need to solve for t when P(t) = 2 * P(0).
2 * P(0) = P(0) * (1 + r)^t
2 = (1 + 0.084)^t
Taking the natural log of both sides:
ln(2) = t * ln(1.084)
t = ln(2) / ln(1.084)
t ≈ 8.24
Therefore, the population of Anytown will double in approximately 8.24 years from 1996, which would be in the year 2005.