Solve
-A Local Pond Can Only Hold Up to 39 $\frac { \mathrm { dP } } { \mathrm { dt } } = ( 0.0013 ) ( 39 - \mathrm { P } ) \mathrm { P }$

question 36

Multiple Choice

Solve.
-A local pond can only hold up to 39 geese. Six geese are introduced into the pond. Assume that the rate of grow of the population is $\frac { \mathrm { dP } } { \mathrm { dt } } = ( 0.0013 ) ( 39 - \mathrm { P } ) \mathrm { P }$ where $t$ is time in weeks. Find a formula for the goose population in terms of $\mathrm { t }$ .

• A) \(\mathrm { P } ( \mathrm { t } ) = \frac { 39 } { 1 + 5.5 \mathrm { e } ^ { - 0.051 \mathrm { t } } }\)
• B) \(P ( t ) = \frac { 39 } { 1 + 33 e ^ { - 39 t } }\)
• C) \(\mathrm { P } ( \mathrm { t } ) = \frac { 39 } { 1 + 5.5 \mathrm { e } ^ { - 39 \mathrm { t } } }\)
• D) \(\mathrm { P } ( \mathrm { t } ) = \frac { 39 } { 1 + 33 \mathrm { e } ^ { - 0.051 \mathrm { t } } }\)

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Definitions:

IQ Tests

Standardized tests designed to measure human intelligence and cognitive abilities.

Standard Deviation

A statistical measure of the dispersion or variability within a data set, indicating how spread out the values are.

Percentile

A statistical value that indicates the relative standing of a data point within a dataset, often used to compare individual scores to a broader population.

Mean

The arithmetic average of a set of numbers, calculated by adding all the numbers together and then dividing by the count of those numbers.