Use the information in Example 1 to determine the year in which the population of San Dieg...

Use the information in Example 1 to determine the year in which the population of San Diego reached 1.1 million people.

EXAMPLE 1

According to data from the U.S. Census Bureau, the approximate population y (in millions) of Detroit is given by

where x = 0 corresponds to 1950. The approximate population of San Diego during the same period is given by

(a) Approximately when did the two cities have the same population?

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(b) In what year was the population of Detroit about 1,500,000?

SOLUTION

(a) The populations of the two cities are equal when

We solve this equation by graphing the left side as y1 and the right side as y2 and finding the intersection point, as in Figure 1. Rounding the x-coordinate to the nearest year (x ≈ 38), we see that the populations were equal around 1988.

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(b) To find when the population of Detroit was 1,500,000 (that is, 1.5 million), we must solve the equation

Since the left side of this equation has already been graphed as y1, we need only graph y3 = 1.5 on the same screen and find the intersection point of y1 and y3, as in Figure 2. The solution x ≈ 20.45 shows that Detroit had a population of 1.5 million in 1970.

Figure 1

Figure 2