The population of Hackens was 593 155 on January 1 2010 and

The population of Hackens was 593, 155 on January 1, 2010, and the population of the city has been decreasing by 2.7 percent each year. a. Determine the 1-year growth factor: b. Determine the 1-year percent change: c. Determine the initial value: d. Define a function f that gives the population of Hackens t years after January 1, 2010. e. Define a function g that gives die population of Hackens n months after January 1, 2010. f. Use the functions you defined above and a graphing calculator to determine in which year the population will reach 354. 755 people. Preview

Solution

population decreasing by 2.7% every year

Intial pop. , P = 593155 on 1 Jan 2010

a) Grwoth factor = 1- x = 1 - 0.027 = 0.973

b) % change in 1 year = 2.7%

c) Intial value = 593155

d) f(t) = 593155(0.973)^t

e) In terms of no. of months:

t( years)= n (months)/12

g(n) = 593155(0.973)^(n/12)