what will be the population 4 years from now?

label Calculus
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Jul 22nd, 2015

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r(t) = 1200 (1+ ((2t)/(1+t^2)) (0 ≤ t ≤ 5)

The increase in population after the 1st year is r(1).

r(1) = 1200 (1+ ((2*1)/(1+1^2)) = 1200(1+2/2) = 1200(1+1)


In the 2nd year, the increase is r(2),.

r(2) = 1200 (1+ ((2*2)/(1+2^2)) = 1200(1+4/5)

In the 3nd year, the increase is r(3),.

r(3) = 1200 (1+ ((2*3)/(1+3^2)) = 1200(1+6/10)

In the 4th year, the increase is r(4),

r(4) = 1200 (1+ ((2*4)/(1+4^2)) = 1200(1+8/17)

After 4 years the population is 35,000 + r(1) + r(2) + r(3) + r(4) + r(5)
= 35000 + 1200[(1+1) + (1 + 4/5) + (1 + 6/10) + (1 + 8/17) + (1+10/26)]
= 35000 + 1200*(6 +0.8+0.6+0.471+0.3846)

=35000+1200*8.2556

=35000+9906.73846
= 44906.738

= approx. 44907


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 23rd, 2015

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