The U.S. population is approximated by the function

Question

P(t) = 616.5/1 + 4.02e^-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 2050 (t = 4)? (Round your answer to the nearest integer.)

_____ million people

Answer 1

Is the function supposed to be P(t) = 616.5/(1 + 4.02e^-0.5t)? I will interpret P(t) this way because this is a logistical growth model, which is more realistic than an unlimited growth model.

You were told what to plug into t. Evaluate P(4):

P(4) = 616.5 / (1 + 4.02e^-0.5(4))

P(4) = 616.5 / (1 + 4.02e^(-2))

P(4) ≈ 616.5 / (1 + 0.54405)

P(4) ≈ 616.5 / 1.54405

P(4) ≈ 399.28

Round this down to 399. This is in millions.

In 2050, the population of the United States will be approximately 399 million people.