The town of Nowhere had a population of 1500 people in 2005

The town of Nowhere had a population of 1,500 people in 2005 and 1,220 people in 2015. What will the population of Nowhere be in the year 2025 assuming the exponential growth model?

Solution

population of Nowhere in 2005 = 1500

Population of Nowhere in 2015=1220

per exponential growth model, population at any time t is given by

P=P_oe^rt ,whete P_o is population at t=0, r=rate of increae of population

at t=2005,P=1500 and at t=2015, P=1220

1500=P_oe^2005r

1220=P_oe^2015r

dividing the above two equations,we get

1500/1220 =e^2005r/ e^2015r=e^-10r

1.229=e^-10r

r = -0.0206

P=Poe^-0.0206t

1500=P_oe^-0.0206*2005

P_o = 1.299*10²¹

therefore, population estimated in 2025=1.299*10²¹e^-0.0206*2025 = 993

therefore, estimated population of Nowhere in year 2025 is 993