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) \(P ( t ) = \frac { 56 } { 1 + 51 e ^ { - 56 t } }\)

---

Definitions:

Suture

A type of joint found in the human skull where bones are joined by a rigid, fibrous connection, or the act of stitching tissues together during surgery.

Syndesmosis

A type of fibrous joint in which two bones are joined together by a ligament or a membrane, allowing for slight movement.

Gomphosis

Fibrous joint in which a peglike process fits into a hole.

Symphysis

A type of cartilaginous joint where bones are fused together by fibrocartilage, providing strength with limited movement.