Chapter 0.1, Problem 48E

Job growth The number of jobs in 2000, the number projected in $2025$, and the projected annual growth rate for jobs in some cities are shown in the following table. Consider the following sets.

$A$

= set of cities with at least $2,000,000$ jobs in $2000$ or projected in $2025$.

$B$

= set of cities with at least $1,500,000$ jobs in $2000$.

$C$

= set of cities with projected annual growth rate of at least $2.5\%$

(a) List $A,B,\text{ and }C$

(using the letters to represent the cities).

(b) Is any of $A,B,\text{ or }C$ a subset of the other?

(c) Find $A\cap C$ and describe the set in words.

(d) Give a verbal description of $B\text{'}$.

$\begin{array}{cccc}& & \text{Projected }& \text{Annual }\\ & \text{Jobs in 2000}& \text{Jobs in 2025}& \text{Rates of}\\ \text{Cities}& \left(\text{thousands}\right)& \left(\text{thousands}\right)& \text{Increase }\left(\text{\%}\right)\\ \text{0 }\left(\text{Orlando}\right)& 1098& 2207& 2.83\\ \text{M }\left(\text{Myrtle Beach}\right)& 133& 256& 2.64\\ \text{L }\left(\text{Atlanta}\right)& 2715& 4893& 2.38\\ \text{P }\left(\text{Phoenix}\right)& 1953& 3675& 2.56\\ \text{B }\left(\text{Boulder}\right)& 233& 420& 2.38\end{array}$

Source: Based on data from NM Data Services, Inc.