Brain weight B as a function of body weight W in fish has been modeled by the power function B=.007W2/3, where B and W are measured in grams. A model for body weight as a function of body length L (measured in cm) is W=.12L2.53. If, over 10 million years, the average length of a certain species of fish evolved from 15cm to 20cm at a constant rate, how fast was the species' brain growing when the average length was 18cm? Round your answer to the nearest hundredth _____nanograms/yr

Question

anonymous · Answer

@phi help please!

anonymous · Answer

@mathmale help please

mathmale · Answer

I'll help if I can.  I'm having trouble deciphering your "W=.12L2.53" and would like to recommend that you either type it into Equation Editor or draw it in the Draw utility.

anonymous · Answer

@mathmale here is the attachment.

mathmale · Answer

Wow!  Some problem.

I see we need to find the rate at which the brain was growing when the average length was 18 cm.

mathmale · Answer

Here's what I see:  We need to find (dB/dL).  Notice that there's no W in there.

As I interpret this problem, B is a function of W, whereas W itself is a function of L.  Does this make sense to you?  Since B is a function of W, we can throw out the variable W and substitute the expression for W as a function of L.  If this does make sense, try doing that.   (eliminate W).

phi · Answer

What steps have you taken so far?

How about these:
Find W when L is 18 cm

use implicit differentiation and your two equation to find dB/dt  and dW/dt

identify dL/dt

can you do those steps?