The data for a is 1900 150000 1990 1300000 2010 1900000 Usin

The data for (a) is

1900: 150000

1990: 1300000

2010: 1900000

Using a search engine or otherwise, find and write down the population for your location, in the years 1900, 1990 and 2010 (or, as close as possible to these years). Use the information found in (a) to create four mathematical models for the city\'s population: Three different models of the form P(t) = at + b, where a and b are to be determined using your data points. One exponential model of the form P(t) = P_0e^kt, where P_0 and k are to be determined using your 1900 data and either your 1990 or 2010 data.

Solution

1900    150000

1990     1300000

2010     1900000

b 1) using data of 1900 and 1990 to find p(t)

p(t) = at + b

a = 1300000 - 150000 / 1990 - 1900

= 115000

b is the initial population which is 150000

p(t) = 115000 t + 150000

b ) 2 )

p(t) = Po e^kt

Po = initial population

P(t) = final population

so , finding value of k

1900000 = 150000 e^110k

1900000 / 150000 = e^110k

12.66 = e^110k

k = ln 12.66 / 110 = .0231

hence, equation is

P(t) = 150000 e^.0231 t