In 1751, Benjamin Franklin predicted that the U.S. population P(t) would increase with growth constant k =

Question:

In 1751, Benjamin Franklin predicted that the U.S. population P(t) would increase with growth constant k = 0.028 year−1. According to the census, the U.S. population was 5 million in 1800 and 76 million in 1900. Assuming logistic growth with k = 0.028, find the predicted carrying capacity for the U.S. population. Use Eqs. (3) and (4) to show that

y y - A = Beki