The population of a certain city was 192000 in 1998, and the observed relative growth rate is 4 percent per year

Question

(a) Find a function that models the population after t years.
Your answer is

 

(b) Find the projected population in the year 2004.
Your answer is

 

(c) In what year will the population reach 411699?
Your answer is

Answer 1

This type of situation is modeled with an exponential function:

 

P(t) = a(r)^t,

 

where P(t) is population after t time periods have passed, a is initial population, r = rate of growth, and t = time periods that have passed.

 

For you, initial population a = 192000 and rate of growth r = 1.04 (since each successive year, the population is 104% of the previous year's population). So, your function is:

 

P(t) = 192000(1.04)^t

 

 

 

To find the population in the year 2004, after 6 years have passed, plug in t = 6 and solve for P(t).

 

 

 

To figure out what year the population will reach 411699, plug in P(t) = 411699 and solve for t. At some point, you'll need to convert to logarithms in order to find the answer.