SOLUTION: can someone help me with this please thanks 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

Question 203088: can someone help me with this please thanks
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 1950 and 1960. In other words:
* Let P = P (t) be the population, where t is the number of years after 1950.
* 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.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 1950 and 1960. In other words:
* Let P = P (t) be the population, where t is the number of years after 1950.
* 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.
---------------
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
========================================================
Cheers,
Stan H.
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