A town population of 23,000 at present grows at an average rate of 2.5% every 8 years.
a)What is the possible population of the town in 25 years?
b)How many people were living in the town 10 years ago?
after t years,
p(t) = 23000 * 1.025^(t/8)
so, p(25) = 24845
p(-10) = 22301
To find the answers to these questions, we need to use the formula for compound interest. In this case, it would represent the population growth of the town.
The formula for calculating compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (population in this case)
P = the principal amount (present population)
r = annual interest rate (growth rate as a decimal)
n = number of times the interest is compounded per year
t = number of years
Now, let's break down the questions:
a) What is the possible population of the town in 25 years?
First, we need to calculate the growth rate per 8 years, since the growth rate is given as such. To do this, we divide the given growth rate (2.5%) by the number of years (8):
growth rate per 8 years = 2.5% / 8 = 0.3125% per year
Now, we substitute the values into the compound interest formula:
A = 23,000(1 + 0.3125/100)^(25/8)
Calculating this equation will give us the possible population of the town in 25 years.
b) How many people were living in the town 10 years ago?
To find this information, we need to subtract the growth over 10 years from the present population.
First, we calculate the growth rate per 8 years as before:
growth rate per 8 years = 2.5% / 8 = 0.3125% per year
Next, we calculate the number of 8-year periods between the present year and 10 years ago:
number of 8-year periods = 10 years / 8 years per period = 1.25 periods
Now, we use the compound interest formula, but this time substituting the number of periods as a negative value since we are going back in time:
A = 23,000(1 + 0.3125/100)^(-1.25)
Calculating this equation will give us the population of the town 10 years ago.
Please note that the calculations provided assume the growth rate is constant and do not take into consideration other factors that might affect population growth.