Question

San Diego is one of the largest cities in the United States. In 2012, the population of San Diego was 1,309,000. By 2016, the population had grown to 1,375,000, and reached 1,386,000 in 2020.(a) What was the growth rate (k) from 2012 to 2016?(b) What was the growth rate (k) from 2016 to 2020?

Answer 1

The growth rate formula is :

$k=(\frac{p_2}{p_1})^{\frac{1}{n}}-1$

where k = growth rate

p2 = future population

p1 = previous population

n = time in years

a. Growth rate from 2012 to 2016

t = 4 years

p2 = 1,375,000

p1 = 1,309,000

The growth rate will be :

$\begin{gathered} k=(\frac{1375000}{1309000})^{\frac{1}{4}}-1 \\ k=0.0124 \end{gathered}$

Multiplied by 100 :

k = 1.24%

b. Growth rate from 2016 to 2020

t = 4 years

p2 = 1,386,000

p1 = 1,375,000

The growth rate will be :

$\begin{gathered} k=(\frac{1386000}{1375000})^{\frac{1}{4}}-1 \\ k=0.0020 \end{gathered}$

Multiplied by 100 :

k = 0.20%