In 2004 the population of a certain city was 21 comma 292

In 2004 , the population of a certain city was 21 comma 292 . If the relative growth rate has been 5.1 % since 1985 , what was the population of the city in 1985 ? Use the exponential growth model Upper P left parenthesis t right parenthesis equals Upper P 0 e Superscript kt Baseline .

Solution

P = pe^(rt) is a population growth function.

r is rate of growth,

p is initial population in 1985,

P in population in 2004 where t = 19

21292 = pe^(0.051* 19)

21292 = pe(0.969)

21292 = p * (2.635)

p = 21292 / 2.635

p = 8080