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A country's population in 1993 was 94 million. in 1999 in was 99 million. estimate the population in 2005 using the exponential growth formula. round your answer to the nearest millionth. P=Ae^kt

Respuesta :

Let P(t) denote the population at t years after 1993, then 

P(0) = 94 million 
P(6) = 99 million 

P(t) = P(0) e^(k t) 

Therefore 

P(6) = P(0) e^(6 k) 

99 = 94 e^(6 k) 

e^(6 k) = 99/94 

6 k = ln (99/94) 

k = ln (99/94) / 6 = 0.0086375 

Now that we have the value of k, we can estimate the populatioin 
in 2005 

t = 2005 - 1993 = 12 

P(12) = P(0) e^( 12 k) = 94 e^( 12 (0.0086375) ) = 104.266 million

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

The estimated population of the country in 2005 is 104 million .

What is the estimated population of the country in 2005?

The first step is to determine the rate of growth of the country.

Rate of growth = [(population in 1999 / population in 1993)^(1/n)] - 1

Where n is the number of years

[(99 / 94)^(1/6)] - 1 = 0.0867

Now the population in 2005 can be determined given the formula in the question.

P=Ae^kt

94 x (1.0867)^12 = 104 million

To learn more about exponential functions, please check: https://brainly.com/question/26331578

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