Final answer:
To find the population of a town after 13 years, given a 4.5% annual growth rate, use the formula for exponential growth with the values: initial population of 2000, growth rate of 4.5% (0.045 in decimal), and time of 13 years. Calculate the future population and round to the nearest whole number.
Step-by-step explanation:
To calculate the future population of a town with a current population of 2000 and an annual growth rate of 4.5%, we will use the formula for exponential growth: P = P0(1 + r)^t, where P is the future population, P0 is the initial population, r is the growth rate (expressed as a decimal), and t is the time in years. In this case, the initial population (P0) is 2000, the growth rate (r) is 4.5%, or 0.045 when converted to a decimal, and the time (t) is 13 years.
Step-by-step calculation:
- Convert the growth rate from a percentage to a decimal: 4.5% = 0.045.
- Apply the formula with the given values: P = 2000(1 + 0.045)^13.
- Calculate the growth factor (1 + 0.045)^13 using a calculator.
- Multiply the initial population by the growth factor to find the future population.
- Round the result to the nearest whole number as requested.
The exact formula with the inserted values will look like this:
P = 2000(1 + 0.045)^13
After performing the calculations, you will find the future population of the town after 13 years, to the nearest whole number.