Question

Population the populations P (in thousands) of Las Vegas Nevada from 1960 through 2009 can be modeled by p = 70.751e 0.0451t, where t is the time in years,with t = 0 corresponding to 1960.

(a) Find the populations in 1960,1970,1980,1990,2000,and 2009.
(b) Explain why the change in population from 1960to 1970 is not the same as the change in population from 1980 to 1990.
(c) Use the model to estimate the population in 2020.

Answer 1

the answer is below

Explanation:

The model is:

`p=70751e^(0.0451t)` where t is the time in years.

a)

• when t=0 (year 1960)
  `p=70751e^(0.0451*0)=70751`

• when t=10 (year 1970)
  `p=70751e^(0.0451*10)=111071`

• when t=20 (year 1980)
  `p=70751e^(0.0451*20)=174368`

• when t=30 (year 1990)
  `p=70751e^(0.0451*30)=273737`

• when t=40 (year 2000)
  `p=70751e^(0.0451*40)=429734`

• when t=49 (year 2009)
  `p=70751e^(0.0451*49)=644882`

b)

The change in population from 1960to 1970 is 111071-70751 =40320

The change in population from 1980 to 1990 is 273737-174368=99369

The change from 1960to 1970 is not the same as the change from 1980 to 1990 because the model function is not linear, it is exponential. Therefore, the rate of the change is not constant.

c)

The population in 2020 using the model can be estimated as

when t=60 (year 2020)
`p=70751e^(0.0451*60)=1059091`