Application of growth/decay

Question

From 1990 to 2006, the population P (in millions) of a large city can be modeled by P = 1.1 * (1.05) ^ t . where t is the number of years since 1990.

a What is the population in 1990?

b. What is the percent of increase each year?

c. What is the expected population in 2002?

Answer 1

(a)

In 1990, t = 0, so the population in 1990 is

P(1990) = 1.1 (1.05)⁰ million = 1.1 million

(b)

It increases by a factor of 1.05 each year, i.e. it increases to 105% of its value at the start of the year, which is an increase of 5% each year.

(c)

From 1990 to 2002, 12 years have elapsed, so t = 12.

P(2002) = 1.1 (1.05)¹² million = 1.975 million