A Local Pond Can Only Hold Up to 56 Geese $\frac { \mathrm { dP } } { \mathrm { dt } } = ( 0.0013 ) ( 56 - \mathrm { P } ) \mathrm { P }$

question 4

Multiple Choice

A local pond can only hold up to 56 geese. Five geese are introduced into the pond. Assume that the rate of growth of the population is $\frac { \mathrm { dP } } { \mathrm { dt } } = ( 0.0013 ) ( 56 - \mathrm { P } ) \mathrm { P }$ where t is time in weeks. Find a formula for the goose population in terms of t.

• A) \(\mathrm { P } ( \mathrm { t } ) = \frac { 56 } { 1 + 51 \mathrm { e } ^ { - 0.073 \mathrm { t } } }\)
• B) \(P ( t ) = \frac { 56 } { 1 + 10.2 e ^ { - 56 t } }\)
• C) \(P ( t ) = \frac { 56 } { 1 + 10.2 e ^ { - 0.073 t } }\)
• D) \(P ( t ) = \frac { 56 } { 1 + 51 e ^ { - 56 t } }\)

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Definitions:

Milk Runs

A logistics strategy where a single vehicle collects loads from several suppliers in a single journey, optimizing transport efficiency and reducing costs.

Supply Chain

The network of organizations involved in producing, handling, and distributing goods or services from production to the end consumer.

Cost

The value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore.

Lead Times

The amount of time that elapses between the initiation and completion of a process, such as the period from placing an order to delivery.