In a favorable habitat and without natural predators, a population of reindeer is introduced to
an island preserve. The reindeer population t years after their introduction in 1990 is given by . F(t)=-0.125t^5+3.125t^4+4000. Estimate the number of reindeer on the island in 2007.
so if 1990 ---> t = 0
then 2007 ---> t = 17
F(17) = sub in t = 17 into your equation and evaluate
well, 2007 is 1990+17, so just plug in 17 for t.
To estimate the number of reindeer on the island in 2007, we need to substitute the value of t = 2007 into the given function F(t) = -0.125t^5 + 3.125t^4 + 4000.
Let's calculate it step by step:
1. Start by substituting t = 2007 into the function:
F(2007) = -0.125(2007)^5 + 3.125(2007)^4 + 4000
2. Calculate the powers of 2007:
2007^5 = 2,221,802,602,043
2007^4 = 16,729,858,704,849
3. Substitute the calculated powers into the function:
F(2007) = -0.125(2,221,802,602,043) + 3.125(16,729,858,704,849) + 4000
4. Simplify the calculations:
F(2007) ≈ -2,777,252,825,255.375 + 52,279,554,651,528.125 + 4000
5. Calculate the final result:
F(2007) ≈ 52,279,554,828,272.75
Therefore, the estimated number of reindeer on the island in 2007 is approximately 52,279,554,828,273.