Given that the approximate population y
(in millions) of Los Angeles between 1950 and 2000 is given by
[tex]y=0.0000113x^3 -0.000922x^2 +0.0538x +1.97[/tex]
where 0 corresponds to 1950.
To determine the year in which the population of Los Angeles reached 2.6 million, we equate the given equation with 2.6 and then solve.
[tex]0.0000113x^3 -0.000922x^2 +0.0538x +1.97=2.6 \\ \\ 0.0000113x^3 -0.000922x^2 +0.0538x -0.63=0[/tex]
To eliminate the decimals, we multiply through by 10,000,000 to get
[tex]113x^3-9,220x^2+538,000x-6,300,000=0[/tex]
Solving the above problem will be quite dificult, but by choosing arbitrary values of x, we can see that
for x = 14:
[tex]113(14)^3-9,220(14)^2+538,000(14)-6,300,000=-265,048[/tex]
for x = 15:
[tex]113(15)^3-9,220(15)^2+538,000(15)-6,300,000=76,875[/tex]
Because, the equation is negative for x = 14 and is positive for x = 15, we can see that the value of x is between 14 and 15.
From the quection, we were told that x = 0 corresponds to 1950. Thus, x = 14 will corespond to 1950 + 14 = 1964.
Therefore, the year in which the population of Los Angeles reached 2.6 million is 1964.
