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? $

## Discussion

## Video Transcript

Okay. Recall the fact that we have our run R two d r one over d, t and D are two over DT in this problem. Therefore, we know we can write out an equation. One over R is one of 11 over 80 plus one over r two. This simplifies to nine over 400 if we hop eight common denominators simplified which gives us our is 400 over nine because of one over ours. Not over 400 men are over. One of just our is 400 over nine. Therefore, we know we can multiply 400 over nine squared comes one over 80 squared times 0.3 plus one over 100 squared times 0.2 and then we know we can simplify to get 0.132 on the November. This is in terms of the units for resistance

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