Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.01 P - 0.0002 P ^ { 2 }$

question 126

Essay

Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0002 P ^ { 2 }$ . Solve this differential equation with the initial condition P(0) = 20.

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Definitions:

Annual Interest Rate

The percentage of interest that will be charged or earned on a sum of money over a one-year period.

Tenth Year-end Deposit

The act of placing funds into a financial account or investment at the end of the tenth year of the account or investment's existence.

Annual Year-end Payments

Payments made at the end of a fiscal year, often related to taxes, dividends, or bonuses.

Interest Rate

The percentage of a sum of money charged for its use, often expressed annually.