Despite control measures, the pigeon population in Summerfield is increasing by 10% each year. If there are currently 8,600 pigeons, how many pigeons will there be in 8 years?If necessary, round your answer to the nearest whole number.
Question
Despite control measures, the pigeon population in Summerfield is increasing by 10% each year. If there are currently 8,600 pigeons, how many pigeons will there be in 8 years?If necessary, round your answer to the nearest whole number.
Solution
To solve this problem, we need to use the formula for compound interest, which is also applicable to population growth. The formula is:
P = P0 * (1 + r)^n
where:
- P is the future value of the investment/loan, including interest
- P0 is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (in decimal)
- n is the number of years the money is invested or borrowed for
In this case:
- P0 = 8600 (the current pigeon population)
- r = 10/100 = 0.1 (the annual growth rate)
- n = 8 (the number of years)
Substituting these values into the formula, we get:
P = 8600 * (1 + 0.1)^8
Now, we just need to calculate the value of P.
- Calculate the value of (1 + 0.1) = 1.1
- Raise 1.1 to the power of 8 to get approximately 2.14358881
- Multiply 8600 by 2.14358881 to get approximately 18428.863
So, there will be approximately 18429 pigeons in Summerfield in 8 years, rounding to the nearest whole number.
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