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Logistic Equation

 

 

Here are some questions that I have made up so you can have additional practice with "Logistic Equation" type problems. It is assumed you have already leaned the basics about these kinds of differential equations and are just looking for extra practice. If you are not familiar with this type of differential equation, please refer to the tutorial on differential equations.

 

 

Practice Problems

1. If y' = 4y (1-y/20) and y(0) = 2, what is y(3)?

 

2. If y' = (1/3)y (1-2y) and y(0) = (1/10), what is the particular solution?

 

3. Find the general solution to y' = (1/4)y (3-y/2).

 

4. A colony of donkeys is introduced to the lagoon area. Initially there are only 5 donkeys but six months later there are 8 donkey foraging around the lagoon. If the carrying capacity of the lagoon is 40 donkeys, how long after being introduced will the donkey population reach its 90% of its maximum?

 

5. A herd of hippos moves into the trash dumpsters behind Tropicana Gardens. Originally it was thought that there were only 3 hippos but currently there are 6 hippos. It is also noticed that the hippos are currently increasing at a rate of 2 per month. If the manufactures of the trash dumpsters claim that 24 hippos can easily fit in their dumpsters, how many hippos will there be in 4 months from now?

 

 

Answers

 

 

By

Lee DeAnda

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