Suppose That a School of Fish in a Pond Grows $\mathrm { P } ( \mathrm { t } ) = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kt } }$

question 34

Short Answer

Suppose that a school of fish in a pond grows according to the exponential law $\mathrm { P } ( \mathrm { t } ) = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kt } }$ and suppose that the size of the colony triples in 24 days. Determine k.
Enter your answer exactly in the form $\frac { \ln a } { \mathrm {~b} }$ where a, b are integers.

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Definitions:

Biological Changes

Transformations or alterations occurring in living organisms as a result of growth, aging, or responses to environmental influences.

Social Changes

Shifts in the structure or culture of a society over time that influence the way individuals or communities interact and function.

Behavioral Changes

Alterations in an individual's actions or reactions, often as a result of learning, experience, or environmental influences.

Childbirth Customs

The practices, rituals, and beliefs associated with the process of giving birth, which vary widely across different cultures and societies.