National Park Service personnel are trying to increase the size of the bison population of the national park. If 287 bison currently live in the park, and if the population's rate of growth is 3 % annually, find how many bison there should be in 11 years.
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Part 1
There should be approximately
enter your response here bison in 11 years. (Round to the nearest whole number as needed.)
To find the number of bison there should be in 11 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount (number of bison), P is the initial amount (287 bison), r is the annual interest rate (3% or 0.03), n is the number of times the interest is compounded per year (assuming it's annually, so n = 1), and t is the number of years (11).
Plugging in the values, we get:
A = 287(1 + 0.03/1)^(1*11)
A = 287(1 + 0.03)^11
A ≈ 287(1.03)^11
A ≈ 287(1.43046721)
A ≈ 410.74
Rounding to the nearest whole number, there should be approximately 411 bison in 11 years.