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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

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

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

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp