On January 1, 1879, Records Show That 500 of a Fish

question 52

Multiple Choice

On January 1, 1879, records show that 500 of a fish called Atlantic striped bass were introduced into the San Francisco Bay.In 1899, the first year fishing for bass was allowed, 100,000 of these bass were caught, representing 10% of the population at the start of 1899.Owing to reproduction, at any moment in time the bass population is growing at a rate proportional to the population at that moment.Write a differential equation satisfied by B(t) , the number of Atlantic striped bass a time t, where t is in years since January 1, 1879 and 0 $\le$ t < 20 and solve it for B(t) .

• A) \(B(t)=500 e^{7.6 t}\)
• B) \(B(t)=500 e^{0.38 t}\)
• C) \(B(t)=500\left(1-e^{0.38 t}\right)\)
• D) \(B(t)=500\left(20-e^{7.6 t}\right)\)

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Definitions:

Profit Maximization

The procedure a corporation uses to ascertain the optimal price and quantity of production for maximum earnings.

Production Function

An economic model expressing the relationship between inputs (like labor and capital) and the quantity of output produced.

Profit Maximization

The process or strategy of adjusting the production and sale of goods and services to achieve the highest possible profit levels.

Production Function

An equation that describes the relationship between the inputs used in production and the output generated from those inputs.