The population of a culture of bacteria is modeled by the logistic equation P (t) = frac{14,250}{1 + 29e – 0.62t} To the nearest tenth, how many days will it take the culture to reach 75% of it’s carrying capacity? What is the carrying capacity? What are the virtues of logistic model?

ediculeN 2021-01-19 Answered
The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t To the nearest tenth, how many days will it take the culture to reach 75% of it’s carrying capacity? What is the carrying capacity? What are the virtues of logistic model?
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hesgidiauE
Answered 2021-01-20 Author has 106 answers

Step1 P(t)=14,2501+29e(062t)
Ast,e062t0
P(t)14,250.

This is the carrying capacity of the bacten`al culture.

To determine the time it take to reach 75% of thr carlying capacity, we write P(t)=34(14,250).

Step 2

14,2501+29e(062t)=34(14,250)
1+29e062t=34
e(062t)=187
t=1062In(87)=72 Hense it takes the bacterial Popylation 72 days to reach 75% of the calling capacity.

Step 3 The growth of any population is curtailed by the amount of resources available. This is better modeled by a logistic S curve rather than an exponential growth model which only works in ideal situations and not for modeling real life situations.

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