Question

The population of a certain city was 112,000 in 1998, and the observed relative growth rate is 4% per year. (a) Find a function that models the population after t years. (b) Find the projected population in the year 2004. (c) In what year will the population reach 200,000

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Now;

From;

P=Poe^kt

Where;

P = population at time=t

Po = population initially present

k = growth rate

t = time taken

a) The function is;

P= 112,000e^0.04t

b) In the year 2004, the population will be

P= 112,000e^0.04(6)

P= 142380

c) 200,000 =112,000 e^0.04t

200,000/112,000 =  e^0.04t

1.786 = e^0.04t

ln 1.786 = ln e^0.04t

ln 1.786= 0.04t

t = ln 1.786/0.04

t = 14.5 years