Question

A city has a CBR of 15 and a CDR of 17. Ignoring

immigration and emigration, when will the popula-
tion of this city double?
(a) 20 years
(b) 35 years
(c) 200 years
(d) 350 years

***this doesn’t make sense to me as the population is declining, so it couldn’t possibly double

Answer 1

To determine when the population of the city will double, we can use the concept of doubling time with the compound annual growth rate (CBR - CDR) formula:

Doubling Time (in years) = ln(2) / (CBR - CDR)

where ln denotes the natural logarithm.

Given:

CBR (Crude Birth Rate) = 15

CDR (Crude Death Rate) = 17

Substitute the values into the formula to find the doubling time:

Doubling Time = ln(2) / (15 - 17)

Now, calculate the doubling time:

Doubling Time ≈ ln(2) / (-2)

Doubling Time ≈ -0.6931 / 2

Doubling Time ≈ -0.34655 years

Since doubling time cannot be negative, let's take the absolute value:

Doubling Time ≈ 0.34655 years

Now, we need to convert this to years. Since there are approximately 365.25 days in a year, we divide 0.34655 by (365.25 days/year) to get the doubling time in years:

Doubling Time (in years) ≈ 0.34655 years / (365.25 days/year)

Doubling Time (in years) ≈ 0.0009478 years

Now, let's determine which option corresponds to this doubling time:

(a) 20 years

(b) 35 years

(c) 200 years

(d) 350 years

The doubling time is approximately 0.0009478 years, which is much less than 1 year. Therefore, the correct option is not provided in the given choices. If you're looking for the closest option, (a) 20 years would be the closest, but the doubling time is actually much shorter.