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The biomass $ B(t) $ of a fish population is the total mass of the members of the population at time $ t. $ It is the product of the number of individuals $ N(t) $ in the population and the average mass $ M $ of a fish at time $ t. $ In the case of guppies, breeding occurs continually. Suppose that at time $ t = 4 $ weeks the population is 820 guppies and is growing at a rate of 50 guppies per week, while the average mass is 1.2 g and is increasing at a rate of 0.14 g/week. At what rate is the biomass increasing when $ t - 4? $

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00:49

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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it's clear. So when you raid here, so you have a B. A. T is equal to enough tee times and of tea. When we write the product rule for the derivative, we get the derivative of on lefty terms. I'm a lefty. Less energy turns the derivative of love. T be plugged in for 40 Can we get 50 terms? 1.2 plus a 20 terms 0.14 and this is equal to one under 74.8 grams per week.

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