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damaskus [11]
3 years ago
13

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

ere 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?
Mathematics
1 answer:
svetoff [14.1K]3 years ago
6 0

Answer: a) 236,000.

b) 2021

Step-by-step 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=\dfrac{\ln(2.3077)}{0.0205}

t=\dfrac{0.836251357528}{0.0205}=40.7927491477\approx41

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

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