Question

The population p (in millions) of Italy from 1990 through 2008 can be approximated by the model p=56.8e^o.oo15t , where t represents the year with t=0 corresponding to 1990

-Find the populations of Italy in 2000 and 2008
-Use the model to predict the populations of Italy in 2015 and 2020

Answer 1

Answers:

• Year 2000: 57.7 millions
• Year 2008: 58.4 millions
• Year 2015: 59.0 millions
• Year 2020: 59.4 millions

Step-by-step explanation:

The given model provides a function that allows to approximate the population of Italy from 1990 through 2008 and predict the populations for other years, assuming validity of the same model over the coming years.

You only need to convert the year into the variable t and subsitute in the model.

1. Calculate t for every year of your interest:

Year t = year - 1990

1990 1990 - 1990 = 0 (initial value)

2000 2000 - 1990 = 10

2008 2008 - 1990 = 18

2015 2015 - 1990 = 25

2020 2020 - 1990 = 30

2. Calculate the population as per the model:

• 
  `p = 56.8e^(0.0015t)`

• t = 10

`p = 56.8e^(0.0015(10))=57.7`

• t = 18

`p = 56.8e^(0.0015(18))=58.4`

• t = 25

`p = 56.8e^(0.0015(25))=59.0`

• t = 30

`p = 56.8e^(0.0015(30))=59.4`