The U.S. population is approximated by the function
P(t) =
556
1 + 3.72e−0.5t
where P(t) is measured in millions of people and t is measured in 30-year intervals, with t = 0 corresponding to 1930. What is the expected population of the United States in 2020 (t = 3)? (Round your answer to the nearest whole number.)
million people
Just evaluate P(3), (sub in 3 wherever you see a t )
btw, is this supposed to be a fraction?
Not a fraction, so 331.7 thank you!!
To find the expected population of the United States in 2020 (t = 3), we need to substitute the value of t into the function P(t).
The given function is:
P(t) = 556 / (1 + 3.72e^(-0.5t))
Substituting t = 3 into the function:
P(3) = 556 / (1 + 3.72e^(-0.5 * 3))
To calculate the population, we need to evaluate this expression:
P(3) = 556 / (1 + 3.72e^(-1.5))
Using a calculator to evaluate the exponential term inside the parentheses:
P(3) = 556 / (1 + 3.72 * 0.22313016014843)
P(3) = 556 / (1 + 0.833681124797696)
P(3) = 556 / 1.833681124797696
P(3) ≈ 303 million people
Therefore, the expected population of the United States in 2020 (t = 3) is approximately 303 million people.