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

question 29

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.Assume that when fishing starts in 1899, the rate at which bass are caught is proportional to the square of the population with constant of proportionality $10^{-6}$ .Write a differential equation satisfied by B(t) , for t > 20.

• A) \(\frac{d B}{d t}=7.6 B-10^{-6} B^{2}\)
• B) \(\frac{d B}{d t}=7.6 B-\frac{10^{-6}}{B^{2}}\)
• C) \(\frac{d B}{d t}=0.38 B-10^{-6} B^{2}\)
• D) \(\frac{d B}{d t}=0.38 B-\frac{10^{-6}}{B^{2}}\)

---

Definitions:

Midpoint Formula

A method used in geometry and economics to find the midpoint or the average of two points on a line segment.

Consumer Expenditure

The total amount spent by consumers on goods and services in a given period.

Total Revenue

The overall amount of money generated from the sale of goods and services before any expenses are subtracted.