Use the following information for questions 1 through 2 The

Use the following information for questions 1 through 2. The city of Portland, OR had a population of 437, 319 in 1990, and a population of 529, 121 in 2000. Find an exponential model for the population of Portland, with t = 0 corresponding to 1990. When will the population of Portland be 582014?

Solution

population in 1990 = 437,319

population in 2000 = 529,121

standard expoential equation is given by

P = Po e^rt

where, P is final population

Po = initial population

r = rate of growth

t = time

initial population = 437,319 at time t=0

in 10 years population has increased to 529,121

529,121 = 437,319 e^10r

solving for r

529,121/ 437,319 = e^10r

1.2099 = e^10r

taking natural log on both sides

ln (1.2099) = 10r

r = .0190

so the expoenntial mode would be

P = 437319 e^ .0190t

2) time when population would be 582014

plug P = 582014 and solve for t

582014 = 437319 e^ .0190t

582014 / 437319 = e^.0190 t

t = 15.043

therefore, population would be 582014 in the year 2005 approx