The population of a certain city was 138000 in 1998,

Question

And the observed relative growth rate is 3 percent per year.

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

Answer is=

(b) Find the projected population in the year 2004.

Answer is=

(c) In what year will the population reach 211180?

Answer is =

Answer 1

(a)

P(t) = 138000 * (1.03)^t

(b)

2004 corresponds to t = 6 so

P(6) = 138000 * (1.03)^6 = 164779

(c) if

P = 211180 = 138000 * (1.03)^t

then

(1.03)^t = 211180/138000

take the ln of both sides and use the rule ln(a^b) = blna

tln(1.03) = ln(211180/138000)

so

t = ln(211180/138000) / ln(1.03) = 14.39

t = 14 corresponds to the year 1998 + 14 = 2012

.,.,