Question

According to data from the U.S. Bureau of the Census, the approximate population y (in millions) of Los Angeles between 1950 and 2000 is given by 649-01-04-00-00_files/i0260000.jpg where 0 corresponds to 1950. Determine the year in which the population of Los Angeles reached 2.6 million.

Answer 1

The year in which the population of Los Angeles reached 2.6 million is 1964.

Explanation:

Answer 2

Given that the approximate population y (in millions) of Los Angeles between 1950 and 2000 is given by

`y=0.0000113x^3 -0.000922x^2 +0.0538x +1.97`
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.

`0.0000113x^3 -0.000922x^2 +0.0538x +1.97=2.6 \\ \\ 0.0000113x^3 -0.000922x^2 +0.0538x -0.63=0`

To eliminate the decimals, we multiply through by 10,000,000 to get

`113x^3-9,220x^2+538,000x-6,300,000=0`

Solving the above problem will be quite dificult, but by choosing arbitrary values of x, we can see that
for x = 14:

`113(14)^3-9,220(14)^2+538,000(14)-6,300,000=-265,048`
for x = 15:

`113(15)^3-9,220(15)^2+538,000(15)-6,300,000=76,875`

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.