Earth Population ? Impossible Bonus Question !

Hello I was wonderign if someone could help me resolve this Problm I am confused about since 2 days now ! 

1. One model of Earth's population is given by 

 

P(t) = 280 / 4+66e ^-0.021t 

 

Do you mean   (The first one is the correct interpretation.)

 

\(P(t) = \frac{280 }{ 4}+66e ^{-0.021t}\\ or\\ P(t) = \frac{280 }{ 4+66e ^{-0.021t}}\)??

 

In the equation, P(t) is the population and t is the number of years after 1980. 

A. According to this model, what was the Earth's population in the year 2001 ? 

I know I have to plug 21 instead of T But I don't know how to deal with this exponant withe the minus ? 

 

I don't understand why the neg exponent is causing a problem.

For the top one

P(21) = 280/4+66*e^(-0.021*21)

for the bottom one

P(21)= 280/(4+66*e^(-0.021*21))

 

B. According to this model, what will the Earth's population in the year 2021 ?     t=41  etc

 

C. Is a bonus question IMPOSSIBLE : If t is very large, say greater than 500, then e^-0.021t = approximatively 0. What does this suggest about the maximum population the Earth can support ( according to this model ) 

As t gets very big  F(t) tends to 280/4 = 70    (with both equations)

 

Here is the graphs to show you what is happening 

https://www.desmos.com/calculator/cdxjt3wiiz

 

I guess the bottom equaton is the one you meant beacuse that is the one with the increasing population but the maximum population is 70.  After that, natural etrition will equal births. So the population will stay stabe.  (according to this model)

 

 

 

I hope that helps you  :))

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