Question

Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by p = 130e0.0205t,where t = 0 corresponds to 1980.

(a) What was the population of Orlando in 2009?
(b) In what year will Orlando have a population of 300,000?

Answer 1

Answer: a) 236,000.

b) 2021

Explanation:

Given : Population Growth The population P (in thousands) of Oriando,Florida from 1980 through 2009 can be modeled by
`p = 130e^(0.0205t)` (1)

where t = 0 corresponds to 1980.

Then , for 2009

t= 2009-1980=29

a. ⇒The population of Phoenix in 2009 =
`p = 130e^(0.0205(29))`

`p = 130e^(0.5945)`

`p =130(1.81212465608)=235.57620529\approx236`

Hence, the population of Orlando in 2009 was about 236,000.

b) Substitute p= 300 in (1) , we get

`300 = 130e^(0.0205t)`

`2.3077= e^(0.0205t)` (Divide both sides by 130)

Taking Natural log on both sides,

`\ln(2.3077) = 0.0205t\\\\\Rightarrow\ t=(\ln(2.3077))/(0.0205)`

`t=(0.836251357528)/(0.0205)=40.7927491477\approx41`

Hence, The year Orlando will have a population of 300,000 =1980+41 =2021