The population of a certain country was approximately 50 million in 1900.150 mil

Question

The population of a certain country was approximately 50 million in 1900.150 million in 1960, and 275 million in 2000. Construct a model for this data by finding a quadratic equation whose graph passes through the points (0.50). (50, 150). and (100.275). Use this model to estimate the population In 2050. Let x be the number of years since 1900 and y be the population in millions. y=n (Use integers or decimals for any numbers in the expression.) According to the model, what will the population be In the year 2050? y = million

Explanation / Answer

quadratic equation which passes through (0,50) , (50,150) , (100,275)

standard quadratic equation is

y = ax^2 + bx + c

plugging the values in the equation and form 3 equations

50 = a(0)^2 + b (0) + c

c = 50

150 = a(50)^2+ b(50) + c ---------------- equation 1

275 =a(100)^2 + b(100) + c ------------------ equation 2

on solving we get

a = 1/200 , b = 7/4

so,

y = (1/200) x^2 + (7/4)x + 50

population in 2050 is

plug x = 150

y = (1/200)(150)^2 + (7/4)(150) + 50 = 425 million

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