Determining population from a density function defined numerically.

1. The quot;Boston By
The Seaquot; Problem
Boston Harbor Dusk

6. Greater Boston can be approximated by a semicircle of radius 8 miles with its
centre on the coast. Moving away from the centre along a radius, the population
density is constant for the first mile. Beyond that, the density starts to decrease
according to the data given in the table, where ρ(r), thousands/mile2 , is the
population density at a distance r miles from the centre.
(a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.
(b) Determine a possible formula for ρ(r). Use this formula to make another
estimate of the population.

7. (a) Using this data and a Riemann sum, estimate the total population living
in the 8 mile radius.