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Numerade Educator



Problem 40 Hard Difficulty

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

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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