The rate of growth of a fish population was modeled by the equation G(t) = 90,000e^-0.6t/(1+5e^-0.6t)^2 where t is measured in years since 2000 and G in kilograms per year. If the biomass was 10,000 kg in the year 2000, what is the predicted biomass for the year 2020?

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A: We will differentiate the function and simplify.   The detailed solution is as follows below:

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A: Let the quantity Pn grown continuously at a rate of 55% per day. Initial quantity is P0=200.

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A: We will find out the required value.

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A: To determine the derivative of the function ex and domain of the derivative.

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Q: 6. How is the instantaneous rate of change found?

A: Answer and explanation is given below..

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.