Question

1. The population of field mouse in a certain area is known to have an increase at a rate proportional to the present population. The initial population of the field mouse has doubled in 2 years. (1). Determine the initial value problem (i.e., differential equation together with initial condition) of describing the population of the field mouse. (Answer: dP/dt = kP, P(0) = P0) (2). Determine the solution of the initial value problem. (Answer: P(t) = P0 2^(t/2)) (3). From item (2), how long time will it take for the population of the field mouse to triple? (Answer: 2 ln 3 / ln 2 ? 3.17 year)

          1. The population of field mouse in a certain area is known to have an increase at a rate proportional to the present population. The initial population of the field mouse has doubled in 2 years.

(1). Determine the initial value problem (i.e., differential equation together with initial condition) of describing the population of the field mouse.
(Answer: dP/dt = kP, P(0) = P0)

(2). Determine the solution of the initial value problem.
(Answer: P(t) = P0 2^(t/2))

(3). From item (2), how long time will it take for the population of the field mouse to triple?
(Answer: 2 ln 3 / ln 2 ? 3.17 year)

1. The population of field mouse in a certain area is known to have an increase at a rate proportional to the present population. The initial population of the field mouse has doubled in 2 years.

(1). Determine the initial value problem (i.e., differential equation together with initial condition) of describing the population of the field mouse.
(Answer: dP/dt = kP, P(0) = P0)

(2). Determine the solution of the initial value problem.
(Answer: P(t) = P0 2^(t/2))

(3). From item (2), how long time will it take for the population of the field mouse to triple?
(Answer: 2 ln 3 / ln 2 ? 3.17 year)

Added by Jose Angel C.

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