Chapter 5.2, Problem 3E

Reminder Round all answers to two decimal places unless otherwise indicated.

Math and the City An article in The New York Times states, "The number of gas stations [in a city] grows only in proportion to the $0.77$ power of population”. This means that the approximate number $G$ of gas stations in a city is a power function of the population $N$, and the power is $k=0.77$. That is, $G=c{N}^{0.77}$, where $c$ is some (as yet) unknown constant. We measure $N$ in millions.

a. If one city is twice as large as another, how do the numbers of gas stations compare?

b. The population of Houston, Texas, is $2.2\text{ million}$ and, according to Yahoo Local, there are $1239$ gas stations in Houston. Use this information to find the value of $c$.

c. Los Angeles has a population of about $3.9\text{ million}$. Using the value of $c$ that you found in part b, estimate the number of gas stations in Los Angeles. Round your answer to the nearest whole number. (Note: According to Yahoo Local, the correct number is $2013$.)