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Brain weight $ B $ as a function of body weight $ W $ in fish has been modeled by the power function $ B = 0.007W^{2/3}, $ where $ B $ and $ W $ are measured in grams. A model for body weight as a function of body length $ L $ (measured in centimeters) is $ W = 0. 12L^{2.53}. $ If, over 10 million years, the average length of a certain species of fish evolved from $ 15 cm $ to $ 20 cm $ at a constant rate, how fast was this species' brain growing when the average length was $ 18 cm? $

$\approx 0.01045$ grams per million years

03:28

Wen Z.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:28

Brain weight $B$ as a func…

03:24

Brain size in fish Brain w…

08:42

$$\begin{array}{c}{\text {…

03:55

BIO Brain Growth A newborn…

00:49

Length of a fish For a fis…

01:37

Solve each problem.The…

03:12

$\cdot \bullet$ BIO Brain …

02:55

Brawn versus brain How is …

02:17

The von Bertalanffy growth…

04:25

Brain Mass The brain mass …

we know that D L over D t would be 20 centimeters minus 15 and then we know it's divided by 10 because we have 10 million years, which gives us 1/2 centimeters per 1,000,000 years. Which means now we can write be as 0.7 times 0.12 2/3 times l to its exponents, which means them we can take the derivatives that would be deep be over d t 0.7 time 0.12 to the 2/3 times 5.0 sex over three out the 2.0 sex over three and then times D'oh divided by d t. We remember the Ellis 18 deal over DT is 1/2. We already established this. Therefore, we have 0.0 1045 grams per 1,000,000 years as our units

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Brain weight $B$ as a function of body weight $W$ in fish hasbeen modele…

Brain size in fish Brain weight $B$ as a function of body weight $W$ in fish…

$$\begin{array}{c}{\text { Life Span As we saw in the previous section, rese…

BIO Brain Growth A newborn baby's brain grows rapidly. In fact,it h…

Length of a fish For a fish that starts life with a length of 1 $\mathrm{cm}…

Solve each problem.The weight of a small fish in grams after $t$ weeks i…

$\cdot \bullet$ BIO Brain Power As you read this problem, your brain is cons…

Brawn versus brain How is the weight of an animal’s brain related to the wei…

The von Bertalanffy growth function

$L(t)=L_{\infty}-\left(L_{\infty…

Brain Mass The brain mass of a human fetus during the last rimester can be a…