The initial mass of a certain species of fish is 7 million tons. The mass of fish, if left alone,...

Question:

The initial mass of a certain species of fish is {eq}7 {/eq} million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of {eq}2/yr {/eq}. However, commercial fishing removes fish mass at a constant rate of {eq}15 {/eq} million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be?

Rate:

Rate is the special ratio which is used to measure the change of one quantity with respect to another quantity. Rate gives an idea that how much one quantity is increased or decreased by changing the other quantity. So to find the rate we need two parameters such that we find the rate of one parameter with respect to another parameter.

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We have given that,

The initial mass of a certain species of fish is {eq}7 {/eq} million tons

When fish is left then the increase rate is... Slopes and Rate of Change

from

Chapter 7 / Lesson 2
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The rate of change is shown through one variable as it changes the function of another variable and can be seen furthermore as location changes as a function of time. Learn more about slopes, rates of change, and the rate of velocity.