The population of a city is growing at an average rate

of 3% per year. In 1990, the population was 45 000.

a) Write an equation that models the growth of the

city. Explain what each part of the equation

represents.

b) Use your equation to determine the population

of the city in 2007.

c) Determine the year during which the population

will have doubled.

d) Suppose the population took only 10 years to

double. What growth rate would be required for

this to have happened?

Question

Fletcher Glover

Mathematics

13 August, 18:12

The population of a city is growing at an average rate

of 3% per year. In 1990, the population was 45 000.

a) Write an equation that models the growth of the

city. Explain what each part of the equation

represents.

b) Use your equation to determine the population

of the city in 2007.

c) Determine the year during which the population

will have doubled.

d) Suppose the population took only 10 years to

double. What growth rate would be required for

this to have happened?

+4

Answers (1)

Know the Answer?

Madilyn Henderson · Answer 1

a. N (y) = 45,000*1.03^ (y-1990)

N (y) = population in year y,

45,000 = poppulation in 1990,

1.03 = yearly growth factor,

y = year y

c. 90,000 = 45,000*1.03 (y-1990)

2 = 1.03^ (y-1990)

(y-1990) * log 1.03 = log 2

(y-1990) = log 2 / log 1.03 = 23.45

y = 2013.45

ans: middle of 2013