A city has a population of 30,000 people. Suppose that each year the population grows by 3.7% . What will the population be after 6 years?
i multiplied 30,000 by 6 then 3.7 and got 7425000 i don't think that's the answer i feel like im missing a step..
You certainly are missing a step. Let the growth rate r=1.037
Year 1: p1 = 30000
year 2: p2 = p1 * 1.037 = 30000 * 1.037 = 3110
year 3: p3 = p2 * 1.037 = 31110 * 1.037 = 32261
Nite that p2 = p1*r
p3 = p2*r = p1 * r^2
see a pattern here? No, go back to your text.
pn = p1 * r^(n-1)
Now you should be able to get p6
To calculate the population after 6 years, you need to apply the annual growth rate to the current population for each year.
Here's the step-by-step approach:
1. Start with the initial population: 30,000.
2. Calculate the growth rate by multiplying the current population by the growth rate percentage. In this case, the growth rate is 3.7%, so it can be calculated as (3.7/100) = 0.037.
3. To find the population after one year, add the growth to the initial population: Population after 1 year = 30,000 + (30,000 x 0.037)
= 30,000 + 1,110
= 31,110
4. Repeat this process for each subsequent year. For example:
Population after 2 years = 31,110 + (31,110 x 0.037)
= 31,110 + 1,150.47
≈ 32,260.47
Population after 3 years = 32,260.47 + (32,260.47 x 0.037)
= 32,260.47 + 1,193.24
≈ 33,453.71
Continue this process for the remaining years.
5. Finally, apply the same process for the last year (6th year):
Population after 6 years = 30,000 + (30,000 x 0.037) + (31,110 x 0.037) + (32,260.47 x 0.037) + ... + (previous year's population x 0.037)
Alternatively, you can use the formula for calculating compound interest to calculate the population after 6 years:
P(n) = P(0) x (1 + r)^n
Where:
P(n) = population after n years
P(0) = initial population
r = growth rate
n = number of years
So plugging in the values:
P(6) = 30,000 x (1 + 0.037)^6
≈ 35,367.12
Therefore, the population after 6 years would be approximately 35,367.