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
y = 0.0000113x^3-0.000922x2 +0.0538x + 1.97
where 0 corresponds to 1950. Determine the year in which the population of Los Angeles reached 2.6 million.

Answer 1

Answer:

The year in which the population of Los Angeles reached 2.6 million is 1965.

Step-by-step explanation:

We are given the approximate population y (in millions) of Los Angeles between 1950 and  2000 is given by:

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

y = Population(in millions)

We are supposed to find the year in which the population of Los Angeles reached 2.6 million.

Substitute y = 2.6

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

The real solution is x=14.77≈15

We are given that 0 corresponds to 1950.

So, 15 corresponds to 1965

Hence the year in which the population of Los Angeles reached 2.6 million is 1965.