(Modeling) Solve each problem. See Examples 5 and 6 ....

(Modeling) Solve each problem. See Examples 5 and 6 .

Baby Boom U.S. population during the years between 1946 and 1964, commonly known as the Baby Boom, can be modeled by the following linear equation.

y = 2.8370 x + 140.83

Here y represents the population in millions as of July 1 of a given year, and x represents number of years after 1946. Thus, x = 0 corresponds to 1946, x = 1 corresponds to 1947, and so on. (Source: U.S. Census Bureau.)

(a) According to the model, what was the U.S. population on July 1, 1952?

(b) In what year did the U.S. population reach 150 million?