U.S. Population YEAR POPULATION 1930: 122,800,000 1940: 131,700,000 1950: 150,70
ID: 2832197 • Letter: U
Question
U.S. Population YEAR POPULATION
1930: 122,800,000
1940: 131,700,000
1950: 150,700,000
1960: 179,300,000
It is estimated that the limiting population that the United States can support is 500,000,000 people. Predict the population for the year 2000 using the logistic growth model on the basis of the data in the years 1940 and 1950. In other words: Let P = P (t) be the population, where t is the number of years after 1940. Assume P (t) is of the form given by the logistic equation. Determine what the value of L must be in this case. Find the exact values of P (0) and P (10) from the U.S. Population table given above. Use these two data points to find the values of b and k in the formula for P (t). Note: Answer to the nearest 1 million people, and do not use commas in your answer.
Explanation / Answer
1950 corresponds to t=0, so P(0) = 150,700,000
1960 corresponds to t=10, so P(10) = 179,300,000
--------------
Equation = ?
slope = (179,300,000 - 150,700,000)/(10) = 28,600,000/10 = 2,860,000
P-intercept = 150,700,000
-----
P(t) = 2,860,000t + 150,700,000
----------------------------
2000 corresponds to t=50, so P(2000)= 293,700,000
===========================================
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.