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Problem 7 Easy Difficulty

Suppose a population grows according to a logistic model with initial population 1000 and carrying 10,000. If the population grows to 2500 after one year, what will the population be after another three years?

Answer

9000

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Video Transcript

it's there. So when you right here. So we're gonna use the pft equation to get 10,000 all over one plus 10,000 minus 1000 over 1000 times eats and negative Katie. Then we just simplify to get 10,000 all over one plus nine e negative, Katie. Then we just made this equal 2 2500 when it's p of one. So we know that this is gonna be equal to one two. You get 2500 times one plus nine e to the negative K this equal to 10,000 and we get nine e to the negative. K is equal to three and we get e to the negative. K is equal to 1/3. We take the Ellen of both sides, then we get negative. Cake is equal to out on of 1/3 when we plug in p A four. Since this asking for three years out for the first year, we get 10,000 over one plus nine e toe l n of 1/3 terms for and we got 9000