91Ó°ÊÓ

To determine the order-of-magnitude estimate of the number of dentists, the following estimates and assumptions are needed:

• The population of the place or city
• The number of patients attended by a dentist in a single day
• The number of working days for a dentist in a year
• The number of times each patient visits the dentist in a year

You may estimate that a dentist attends 10 patients in one day, works 225 days a year, and is visited by each patient twice a year.

The order-of-magnitude estimate of a physical quantity is the estimate rounded to the nearest power of 10.

The number of dentists can be determined as follows:

$\begin{array}{c}N=\left(9×{10}^6\mathrm{people}\right)\left(\frac{2\frac{\mathrm{visits}}{\mathrm{year}}}{1\mathrm{person}}\right)\left(\frac{1\mathrm{year}}{225\mathrm{working}\mathrm{days}}\right)\left(\frac{1\mathrm{dentist}}{10\frac{\mathrm{visits}}{\mathrm{workday}}}\right)\\ =8000\mathrm{dentists}\end{array}$

Thus, the estimated number of dentists in San Francisco is 8000.

The number of dentists can be determined by the method used in part (a).

$\begin{array}{c}N=\left(7×{10}^6\mathrm{people}\right)\left(\frac{2\frac{\mathrm{visits}}{\mathrm{year}}}{1\mathrm{person}}\right)\left(\frac{1\mathrm{year}}{225\mathrm{working}\mathrm{days}}\right)\left(\frac{1\mathrm{dentist}}{10\frac{\mathrm{visits}}{\mathrm{workday}}}\right)\\ ≈6222\mathrm{dentists}\end{array}$

Thus, the estimated number of dentists in Massachusetts is 6,000.