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Answer: The population in 2025 will be 7669
Step-by-step explanation:
a) When we have an initial quantity A, and we have an increase of the X%, the new quantity is written as:
new quantity = A + A*(X%/100%) = A*(1 + X%/100%)
In this case, our initial quantity is 3500, the town's population in 2005.
And X% = 4%.
We know that each year, the population increases by 4%.
Then if P(1) is the population one year after 2005, this is:
P(1) = 3500*(1 + 4%/100%) = 3500*(1.04)
After another year, the population increases again:
P(2) = (3500*(1.04))*(1 + 4%/100%)) = 3500*(1.04)*(1.04) = 3500*(1.04)^2
Well, we already can see the pattern here, the population N years after 2005 will be:
P(N) = 3500*(1.04)^N
b) Now we want to know the population in 2025.
N represents the number of years after 2005, then we will have:
N = 2025 - 2005 = 20
2025 is 20 years after 2005.
Then the population in 2025 will be:
P(20) = 3500*(1.04)^20 = 7,668.9
And we can not have a 0.9 of a person, so we should round it up to the next whole number, then the population in 2025 will be 7669